10.07.2015
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714 BIBLIOGRAPHY[274] È. B. Vinberg. The theory of convex homogeneous cones.Transactions of the Moscow Mathematical Society, 12:340–403, 1963.American Mathematical Society and London Mathematical Societyjoint translation, 1965.[275] Marie A. Vitulli. A brief history of linear algebra and matrix theory,2004.darkwing.uoregon.edu/∼vitulli/441.sp04/LinAlgHistory.html[276] John von Neumann. Functional Operators, Volume II: The Geometryof Orthogonal Spaces. Princeton University Press, 1950. Reprintedfrom mimeographed lecture notes first distributed in 1933.[277] Roger Webster. Convexity. Oxford University Press, 1994.[278] Kilian Q. Weinberger and Lawrence K. Saul. Unsupervised learning ofimage manifolds by semidefinite programming. In Proceedings of theIEEE Computer Society Conference on Computer Vision and PatternRecognition, volume 2, pages 988–995, 2004.http://www.cis.upenn.edu/∼lsaul/papers/sde cvpr04.pdf[279] Eric W. Weisstein. Mathworld – A Wolfram Web Resource, 2007.http://mathworld.wolfram.com/search[280] Bernard Widrow and Samuel D. Stearns. Adaptive Signal Processing.Prentice-Hall, 1985.[281] Norbert Wiener. On factorization of matrices. CommentariiMathematici Helvetici, 29:97–111, 1955.[282] Ami Wiesel, Yonina C. Eldar, and Shlomo Shamai (Shitz). Semidefiniterelaxation for detection of 16-QAM signaling in MIMO channels. IEEESignal Processing Letters, 12(9):653–656, September 2005.[283] Michael P. Williamson, Timothy F. Havel, and Kurt Wüthrich.Solution conformation of proteinase inhibitor IIA from bull seminalplasma by 1 H nuclear magnetic resonance and distance geometry.Journal of Molecular Biology, 182:295–315, 1985.[284] Willie W. Wong. Cayley-Menger determinant and generalizedN-dimensional Pythagorean theorem, November 2003.
BIBLIOGRAPHY 715http://www.princeton.edu/∼wwong/papers/gp-r.pdfApplication of Linear Algebra: Notes on Talk given to PrincetonUniversity Math Club.[285] William Wooton, Edwin F. Beckenbach, and Frank J. Fleming. ModernAnalytic Geometry. Houghton Mifflin, 1975.[286] Margaret H. Wright. The interior-point revolution in optimization:History, recent developments, and lasting consequences. Bulletin ofthe American Mathematical Society, 42(1):39–56, January 2005.[287] Stephen J. Wright. Primal-Dual Interior-Point Methods. SIAM, 1997.[288] Shao-Po Wu. max-det Programming with Applications in MagnitudeFilter Design. A dissertation submitted to the department of ElectricalEngineering, Stanford University, December 1997.[289] Shao-Po Wu and Stephen Boyd. sdpsol: A parser/solver forsemidefinite programming and determinant maximization problemswith matrix structure. User’s guide, 1996.http://www.stanford.edu/∼boyd/SDPSOL.html[290] Shao-Po Wu and Stephen Boyd. sdpsol: A parser/solver forsemidefinite programs with matrix structure. In Laurent El Ghaouiand Silviu-Iulian Niculescu, editors, Advances in Linear MatrixInequality Methods in Control, chapter 4, pages 79–91. SIAM, 2000.http://www.stanford.edu/∼boyd/sdpsol.html[291] Shao-Po Wu, Stephen Boyd, and Lieven Vandenberghe. FIR filterdesign via spectral factorization and convex optimization, 1997.http://www.stanford.edu/∼boyd/reports/magdes.pdf[292] Naoki Yamamoto and Maryam Fazel. A computational approach toquantum encoder design for purity optimization, 2006.http://arxiv.org/abs/quant-ph/0606106[293] David D. Yao, Shuzhong Zhang, and Xun Yu Zhou. Stochasticlinear-quadratic control via primal-dual semidefinite programming.SIAM Review, 46(1):87–111, March 2004. Erratum: p.193 herein.
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DATTORROCONVEXOPTIMIZATION&EUCLIDEA
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Convex Optimization&Euclidean Dista
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for Jennie Columba♦Antonio♦♦&
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PreludeThe constant demands of my d
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Convex Optimization&Euclidean Dista
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CONVEX OPTIMIZATION & EUCLIDEAN DIS
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List of Figures1 Overview 191 Orion
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LIST OF FIGURES 1559 Quadratic func
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LIST OF FIGURES 17E Projection 5791
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Chapter 1OverviewConvex Optimizatio
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ˇx 4ˇx 3ˇx 2Figure 2: Applicatio
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23Figure 4: This coarsely discretiz
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ases (biorthogonal expansion). We e
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27Figure 7: These bees construct a
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its membership to the EDM cone. The
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31appendicesProvided so as to be mo
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Chapter 2Convex geometryConvexity h
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2.1. CONVEX SET 35Figure 9: A slab
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2.1. CONVEX SET 372.1.6 empty set v
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2.1. CONVEX SET 392.1.7.1 Line inte
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2.1. CONVEX SET 41(a)R 2(b)R 3(c)(d
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2.1. CONVEX SET 43This theorem in c
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2.2. VECTORIZED-MATRIX INNER PRODUC
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2.2. VECTORIZED-MATRIX INNER PRODUC
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2.2. VECTORIZED-MATRIX INNER PRODUC
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2.2. VECTORIZED-MATRIX INNER PRODUC
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2.3. HULLS 53Figure 12: Convex hull
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2.3. HULLS 55Aaffine hull (drawn tr
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2.3. HULLS 57The union of relative
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2.4. HALFSPACE, HYPERPLANE 59of dim
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2.4. HALFSPACE, HYPERPLANE 61H +ay
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2.4. HALFSPACE, HYPERPLANE 63Inters
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2.4. HALFSPACE, HYPERPLANE 65Conver
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2.4. HALFSPACE, HYPERPLANE 67A 1A 2
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2.4. HALFSPACE, HYPERPLANE 69tradit
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2.4. HALFSPACE, HYPERPLANE 71There
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2.5. SUBSPACE REPRESENTATIONS 732.5
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2.5. SUBSPACE REPRESENTATIONS 752.5
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2.6. EXTREME, EXPOSED 77In other wo
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2.6. EXTREME, EXPOSED 792.6.1 Expos
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2.7. CONES 812.6.1.3.1 Definition.
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2.7. CONES 830Figure 24: Boundary o
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2.7. CONES 852.7.2 Convex coneWe ca
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2.7. CONES 87Thus the simplest and
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2.7. CONES 89nomenclature generaliz
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2.8. CONE BOUNDARY 91Proper cone {0
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2.8. CONE BOUNDARY 93the same extre
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96 CHAPTER 2. CONVEX GEOMETRYBCADFi
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98 CHAPTER 2. CONVEX GEOMETRYThe po
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100 CHAPTER 2. CONVEX GEOMETRY2.9.0
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102 CHAPTER 2. CONVEX GEOMETRYwhere
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104 CHAPTER 2. CONVEX GEOMETRY√2
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106 CHAPTER 2. CONVEX GEOMETRYwhich
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108 CHAPTER 2. CONVEX GEOMETRY2.9.2
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110 CHAPTER 2. CONVEX GEOMETRYA con
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2.9. POSITIVE SEMIDEFINITE (PSD) CO
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2.9. POSITIVE SEMIDEFINITE (PSD) CO
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2.9. POSITIVE SEMIDEFINITE (PSD) CO
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2.10. CONIC INDEPENDENCE (C.I.) 121
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2.10. CONIC INDEPENDENCE (C.I.) 123
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2.10. CONIC INDEPENDENCE (C.I.) 125
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2.12. CONVEX POLYHEDRA 127It follow
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2.12. CONVEX POLYHEDRA 129Coefficie
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2.12. CONVEX POLYHEDRA 1312.12.3 Un
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2.12. CONVEX POLYHEDRA 133
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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2.13. DUAL CONE & GENERALIZED INEQU
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Chapter 3Geometry of convex functio
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3.1. CONVEX FUNCTION 185f 1 (x)f 2
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3.1. CONVEX FUNCTION 1873.1.3 norm
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3.1. CONVEX FUNCTION 189where the n
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3.1. CONVEX FUNCTION 191where k ∈
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3.1. CONVEX FUNCTION 193f(z)Az 2z 1
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3.1. CONVEX FUNCTION 195{a T z 1 +
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3.1. CONVEX FUNCTION 197When an epi
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3.1. CONVEX FUNCTION 199orthonormal
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3.1. CONVEX FUNCTION 201[30,1.1] Ex
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3.1. CONVEX FUNCTION 20321.510.5Y 2
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3.1. CONVEX FUNCTION 2053.1.8.0.1 E
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3.1. CONVEX FUNCTION 207This equiva
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3.1. CONVEX FUNCTION 2093.1.8.1 mon
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3.1. CONVEX FUNCTION 211[ Yt]∈ ep
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3.1. CONVEX FUNCTION 213→Y −Xwh
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3.2. MATRIX-VALUED CONVEX FUNCTION
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3.2. MATRIX-VALUED CONVEX FUNCTION
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3.2. MATRIX-VALUED CONVEX FUNCTION
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3.3. QUASICONVEX 221A quasiconcave
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3.4. SALIENT PROPERTIES 2236.A nonn
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Chapter 4Semidefinite programmingPr
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4.1. CONIC PROBLEM 227where K is a
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4.1. CONIC PROBLEM 229C0PΓ 1Γ 2S+
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4.1. CONIC PROBLEM 231faces of S 3
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4.1. CONIC PROBLEM 2334.1.1.3 Previ
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4.2. FRAMEWORK 235Equivalently, pri
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4.2. FRAMEWORK 237is positive semid
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4.2. FRAMEWORK 239Optimal value of
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4.2. FRAMEWORK 2414.2.3.0.2 Example
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4.2. FRAMEWORK 243where δ is the m
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4.2. FRAMEWORK 2454.2.3.0.3 Example
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4.3. RANK REDUCTION 2474.3 Rank red
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4.3. RANK REDUCTION 249A rank-reduc
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4.3. RANK REDUCTION 251(t ⋆ i)
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4.3. RANK REDUCTION 2534.3.3.0.1 Ex
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4.3. RANK REDUCTION 2554.3.3.0.2 Ex
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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4.4. RANK-CONSTRAINED SEMIDEFINITE
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Chapter 5Euclidean Distance MatrixT
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5.2. FIRST METRIC PROPERTIES 291cor
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5.3. ∃ FIFTH EUCLIDEAN METRIC PRO
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5.3. ∃ FIFTH EUCLIDEAN METRIC PRO
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5.4. EDM DEFINITION 297The collecti
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5.4. EDM DEFINITION 2995.4.2 Gram-f
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5.4. EDM DEFINITION 301D ∈ EDM N
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5.4. EDM DEFINITION 3035.4.2.2.1 Ex
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5.4. EDM DEFINITION 305ten affine e
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5.4. EDM DEFINITION 307spheres:Then
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5.4. EDM DEFINITION 309By eliminati
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5.4. EDM DEFINITION 311whereΦ ij =
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5.4. EDM DEFINITION 3135.4.2.2.5 De
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5.4. EDM DEFINITION 315105ˇx 4ˇx
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5.4. EDM DEFINITION 317corrected by
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5.4. EDM DEFINITION 319aptly be app
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5.4. EDM DEFINITION 321As before, a
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5.4. EDM DEFINITION 323where ([√t
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5.4. EDM DEFINITION 325because (A.3
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5.5. INVARIANCE 3275.5.1.0.1 Exampl
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5.6. INJECTIVITY OF D & UNIQUE RECO
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5.6. INJECTIVITY OF D & UNIQUE RECO
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5.6. INJECTIVITY OF D & UNIQUE RECO
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5.7. EMBEDDING IN AFFINE HULL 3355.
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5.7. EMBEDDING IN AFFINE HULL 337Fo
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5.7. EMBEDDING IN AFFINE HULL 3395.
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5.8. EUCLIDEAN METRIC VERSUS MATRIX
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5.8. EUCLIDEAN METRIC VERSUS MATRIX
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5.8. EUCLIDEAN METRIC VERSUS MATRIX
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5.8. EUCLIDEAN METRIC VERSUS MATRIX
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5.9. BRIDGE: CONVEX POLYHEDRA TO ED
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5.9. BRIDGE: CONVEX POLYHEDRA TO ED
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5.9. BRIDGE: CONVEX POLYHEDRA TO ED
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5.9. BRIDGE: CONVEX POLYHEDRA TO ED
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5.10. EDM-ENTRY COMPOSITION 357(ii)
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5.11. EDM INDEFINITENESS 3595.11.1
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5.11. EDM INDEFINITENESS 361(confer
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5.11. EDM INDEFINITENESS 363we have
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5.11. EDM INDEFINITENESS 365For pre
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5.12. LIST RECONSTRUCTION 367where
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5.12. LIST RECONSTRUCTION 369(a)(c)
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5.13. RECONSTRUCTION EXAMPLES 371D
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5.13. RECONSTRUCTION EXAMPLES 373Th
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5.13. RECONSTRUCTION EXAMPLES 375wh
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5.14. FIFTH PROPERTY OF EUCLIDEAN M
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5.14. FIFTH PROPERTY OF EUCLIDEAN M
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5.14. FIFTH PROPERTY OF EUCLIDEAN M
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5.14. FIFTH PROPERTY OF EUCLIDEAN M
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5.14. FIFTH PROPERTY OF EUCLIDEAN M
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Chapter 6EDM coneFor N > 3, the con
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6.1. DEFINING EDM CONE 3896.1 Defin
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6.2. POLYHEDRAL BOUNDS 391This cone
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6.3.√EDM CONE IS NOT CONVEX 393N
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6.4. A GEOMETRY OF COMPLETION 3956.
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6.4. A GEOMETRY OF COMPLETION 397(a
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6.4. A GEOMETRY OF COMPLETION 399Fi
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6.5. EDM DEFINITION IN 11 T 401and
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6.5. EDM DEFINITION IN 11 T 403then
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6.5. EDM DEFINITION IN 11 T 4056.5.
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6.5. EDM DEFINITION IN 11 T 407D =
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6.6. CORRESPONDENCE TO PSD CONE S N
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6.6. CORRESPONDENCE TO PSD CONE S N
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6.6. CORRESPONDENCE TO PSD CONE S N
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6.7. VECTORIZATION & PROJECTION INT
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6.7. VECTORIZATION & PROJECTION INT
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6.8. DUAL EDM CONE 419When the Fins
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6.8. DUAL EDM CONE 421Proof. First,
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6.8. DUAL EDM CONE 423EDM 2 = S 2 h
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6.8. DUAL EDM CONE 425whose veracit
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6.8. DUAL EDM CONE 4276.8.1.3.1 Exe
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6.8. DUAL EDM CONE 429has dual affi
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6.8. DUAL EDM CONE 4316.8.1.7 Schoe
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6.9. THEOREM OF THE ALTERNATIVE 433
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6.10. POSTSCRIPT 435When D is an ED
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Chapter 7Proximity problemsIn summa
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In contrast, order of projection on
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441HS N h0EDM NK = S N h ∩ R N×N
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4437.0.3 Problem approachProblems t
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7.1. FIRST PREVALENT PROBLEM: 445fi
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7.1. FIRST PREVALENT PROBLEM: 4477.
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7.1. FIRST PREVALENT PROBLEM: 449di
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7.1. FIRST PREVALENT PROBLEM: 4517.
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7.1. FIRST PREVALENT PROBLEM: 453wh
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7.1. FIRST PREVALENT PROBLEM: 455Th
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7.2. SECOND PREVALENT PROBLEM: 457O
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7.2. SECOND PREVALENT PROBLEM: 459S
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7.2. SECOND PREVALENT PROBLEM: 461r
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7.2. SECOND PREVALENT PROBLEM: 463c
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7.2. SECOND PREVALENT PROBLEM: 4657
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7.3. THIRD PREVALENT PROBLEM: 467fo
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7.3. THIRD PREVALENT PROBLEM: 469a
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7.3. THIRD PREVALENT PROBLEM: 4717.
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7.3. THIRD PREVALENT PROBLEM: 4737.
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7.3. THIRD PREVALENT PROBLEM: 475Ou
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478 CHAPTER 7. PROXIMITY PROBLEMSth
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480 APPENDIX A. LINEAR ALGEBRAA.1.1
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482 APPENDIX A. LINEAR ALGEBRAA.1.2
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484 APPENDIX A. LINEAR ALGEBRAonly
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486 APPENDIX A. LINEAR ALGEBRA(AB)
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488 APPENDIX A. LINEAR ALGEBRAA.3.1
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490 APPENDIX A. LINEAR ALGEBRAFor A
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492 APPENDIX A. LINEAR ALGEBRADiago
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494 APPENDIX A. LINEAR ALGEBRAFor A
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496 APPENDIX A. LINEAR ALGEBRAA.3.1
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498 APPENDIX A. LINEAR ALGEBRAA.4 S
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500 APPENDIX A. LINEAR ALGEBRAA.4.0
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502 APPENDIX A. LINEAR ALGEBRAA.5 e
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504 APPENDIX A. LINEAR ALGEBRAs i w
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506 APPENDIX A. LINEAR ALGEBRAA.6.2
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508 APPENDIX A. LINEAR ALGEBRAΣq 2
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510 APPENDIX A. LINEAR ALGEBRAA.7 Z
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512 APPENDIX A. LINEAR ALGEBRAThere
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514 APPENDIX A. LINEAR ALGEBRAA.7.5
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516 APPENDIX A. LINEAR ALGEBRA
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518 APPENDIX B. SIMPLE MATRICESB.1
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520 APPENDIX B. SIMPLE MATRICESProo
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522 APPENDIX B. SIMPLE MATRICESB.1.
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524 APPENDIX B. SIMPLE MATRICESN(u
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526 APPENDIX B. SIMPLE MATRICESDue
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528 APPENDIX B. SIMPLE MATRICESB.4.
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530 APPENDIX B. SIMPLE MATRICEShas
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532 APPENDIX B. SIMPLE MATRICESFigu
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534 APPENDIX B. SIMPLE MATRICESB.5.
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536 APPENDIX C. SOME ANALYTICAL OPT
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538 APPENDIX C. SOME ANALYTICAL OPT
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540 APPENDIX C. SOME ANALYTICAL OPT
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542 APPENDIX C. SOME ANALYTICAL OPT
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544 APPENDIX C. SOME ANALYTICAL OPT
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546 APPENDIX C. SOME ANALYTICAL OPT
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548 APPENDIX C. SOME ANALYTICAL OPT
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Page 550 and 551:
550 APPENDIX D. MATRIX CALCULUSThe
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552 APPENDIX D. MATRIX CALCULUSGrad
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554 APPENDIX D. MATRIX CALCULUSBeca
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556 APPENDIX D. MATRIX CALCULUSwhic
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558 APPENDIX D. MATRIX CALCULUS⎡
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560 APPENDIX D. MATRIX CALCULUS→Y
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562 APPENDIX D. MATRIX CALCULUSD.1.
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564 APPENDIX D. MATRIX CALCULUSwhic
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566 APPENDIX D. MATRIX CALCULUSIn t
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568 APPENDIX D. MATRIX CALCULUSD.1.
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570 APPENDIX D. MATRIX CALCULUSD.2
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572 APPENDIX D. MATRIX CALCULUSalge
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574 APPENDIX D. MATRIX CALCULUStrac
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Page 576 and 577:
576 APPENDIX D. MATRIX CALCULUSD.2.
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Page 578 and 579:
578 APPENDIX D. MATRIX CALCULUS
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Page 580 and 581:
580 APPENDIX E. PROJECTIONThe follo
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582 APPENDIX E. PROJECTIONFor matri
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584 APPENDIX E. PROJECTION(⇐) To
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Page 586 and 587:
586 APPENDIX E. PROJECTIONNonorthog
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Page 588 and 589:
588 APPENDIX E. PROJECTIONE.2.0.0.1
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590 APPENDIX E. PROJECTIONE.3.2Orth
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592 APPENDIX E. PROJECTIONE.3.5Unif
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594 APPENDIX E. PROJECTIONE.4 Algeb
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596 APPENDIX E. PROJECTIONa ∗ 2K
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598 APPENDIX E. PROJECTIONwhere Y =
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Page 600 and 601:
600 APPENDIX E. PROJECTION(B.4.2).
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602 APPENDIX E. PROJECTIONis a nono
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Page 604 and 605:
604 APPENDIX E. PROJECTIONE.6.4.1Or
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606 APPENDIX E. PROJECTIONq i q T i
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Page 608 and 609:
608 APPENDIX E. PROJECTIONThe test
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Page 610 and 611:
610 APPENDIX E. PROJECTIONPerpendic
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Page 612 and 613:
612 APPENDIX E. PROJECTIONE.8 Range
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Page 614 and 615:
614 APPENDIX E. PROJECTIONAs for su
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Page 616 and 617:
616 APPENDIX E. PROJECTIONWith refe
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Page 618 and 619:
618 APPENDIX E. PROJECTIONProjectio
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Page 620 and 621:
620 APPENDIX E. PROJECTIONE.9.2.2.2
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Page 622 and 623:
622 APPENDIX E. PROJECTIONThe foreg
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624 APPENDIX E. PROJECTION❇❇❇
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Page 626 and 627:
626 APPENDIX E. PROJECTIONE.10 Alte
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Page 628 and 629:
628 APPENDIX E. PROJECTIONbH 1H 2P
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630 APPENDIX E. PROJECTIONa(a){y |
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Page 632 and 633:
632 APPENDIX E. PROJECTION(a feasib
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634 APPENDIX E. PROJECTIONwhile, th
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636 APPENDIX E. PROJECTIONE.10.2.1.
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638 APPENDIX E. PROJECTION10 0dist(
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640 APPENDIX E. PROJECTIONE.10.3.1D
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642 APPENDIX E. PROJECTIONE 3K ⊥
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Page 644 and 645:
644 APPENDIX E. PROJECTION
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Page 646 and 647:
646 APPENDIX F. MATLAB PROGRAMSif n
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Page 648 and 649:
648 APPENDIX F. MATLAB PROGRAMSend%
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Page 650 and 651:
650 APPENDIX F. MATLAB PROGRAMSF.1.
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Page 652 and 653:
652 APPENDIX F. MATLAB PROGRAMScoun
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654 APPENDIX F. MATLAB PROGRAMSF.3
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656 APPENDIX F. MATLAB PROGRAMSF.3.
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Page 658 and 659:
658 APPENDIX F. MATLAB PROGRAMS% so
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660 APPENDIX F. MATLAB PROGRAMS% tr
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662 APPENDIX F. MATLAB PROGRAMSF.4.
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Page 664 and 665:
664 APPENDIX F. MATLAB PROGRAMSbrea
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Page 666 and 667:
666 APPENDIX F. MATLAB PROGRAMSwhil
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Page 668 and 669:
668 APPENDIX F. MATLAB PROGRAMSF.7
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Page 670 and 671:
670 APPENDIX F. MATLAB PROGRAMS
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Page 672 and 673:
672 APPENDIX G. NOTATION AND A FEW
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Page 674 and 675:
674 APPENDIX G. NOTATION AND A FEW
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Page 676 and 677:
676 APPENDIX G. NOTATION AND A FEW
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Page 678 and 679:
678 APPENDIX G. NOTATION AND A FEW
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Page 680 and 681:
680 APPENDIX G. NOTATION AND A FEW
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Page 682 and 683:
682 APPENDIX G. NOTATION AND A FEW
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Page 684 and 685:
684 APPENDIX G. NOTATION AND A FEW
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Page 686 and 687:
686 APPENDIX G. NOTATION AND A FEW
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Page 688 and 689:
688 BIBLIOGRAPHY[7] Abdo Y. Alfakih
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Page 690 and 691:
690 BIBLIOGRAPHY[27] Aharon Ben-Tal
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Page 692 and 693:
692 BIBLIOGRAPHY[48] Lev M. Brègma
-
Page 694 and 695:
694 BIBLIOGRAPHY[67] Joel Dawson, S
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Page 696 and 697:
696 BIBLIOGRAPHY[85] Alan Edelman,
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Page 698 and 699:
698 BIBLIOGRAPHY[102] Philip E. Gil
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Page 700 and 701:
700 BIBLIOGRAPHYWeiss, editors, Pol
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Page 702 and 703:
702 BIBLIOGRAPHY[146] Jean-Baptiste
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Page 704 and 705:
704 BIBLIOGRAPHY[168] Jean B. Lasse
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Page 706 and 707:
706 BIBLIOGRAPHY[189] Rudolf Mathar
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Page 708 and 709:
708 BIBLIOGRAPHY[211] M. L. Overton
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Page 710 and 711:
710 BIBLIOGRAPHY[229] C. K. Rushfor
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Page 712 and 713:
712 BIBLIOGRAPHY[252] Jos F. Sturm
-
Page 716 and 717:
[294] Yinyu Ye. Semidefinite progra
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Page 718 and 719:
718 INDEXobtuse, 62positive semidef
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Page 720 and 721:
720 INDEXelliptope, 642orthant, 177
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Page 722 and 723:
722 INDEXdistancegeometry, 20, 317m
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Page 724 and 725:
724 INDEX-dimensional, 37, 89rank,
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Page 726 and 727:
726 INDEXGram form, 331is, 674isedm
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Page 728 and 729:
728 INDEXdiscretized, 152, 431in su
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Page 730 and 731:
730 INDEXboundary, 115dimension, 10
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Page 732 and 733:
732 INDEXlinear operator, 587, 591,
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Page 734 and 735:
734 INDEXlargest entries, 188monoto
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Page 736:
736 INDEXsimilarity, 606translation
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