v2009.01.01 - Convex Optimization
v2009.01.01 - Convex Optimization v2009.01.01 - Convex Optimization
720 APPENDIX F. NOTATION AND A FEW DEFINITIONS ‖x‖ ∞ = max{|x j | ∀j} infinity-norm ‖x‖ 2 2 = x T x = 〈x , x〉 ‖x‖ 1 = 1 T |x| 1-norm, dual infinity-norm ‖x‖ 0 0-norm (4.5.1), cardinality of vector x , card x ≡ ‖x‖ 0 , 0 0 = ∆ 0 ‖X‖ 2 = sup ‖Xa‖ 2 = σ 1 = √ λ(X T X) 1 ‖a‖=1 matrix 2-norm (spectral norm), largest singular value, ‖Xa‖ 2 ≤ ‖X‖ 2 ‖a‖ 2 [134, p.56], ‖δ(x)‖ 2 = ‖x‖ ∞ ‖X‖ = ‖X‖ F Frobenius’ matrix norm
Bibliography [1] Suliman Al-Homidan and Henry Wolkowicz. Approximate and exact completion problems for Euclidean distance matrices using semidefinite programming, April 2004. orion.math.uwaterloo.ca/∼hwolkowi/henry/reports/edmapr04.ps [2] Faiz A. Al-Khayyal and James E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2):273–286, May 1983. http://www.convexoptimization.com/TOOLS/Falk.pdf [3] Abdo Y. Alfakih. On the uniqueness of Euclidean distance matrix completions. Linear Algebra and its Applications, 370:1–14, 2003. [4] Abdo Y. Alfakih. On the uniqueness of Euclidean distance matrix completions: the case of points in general position. Linear Algebra and its Applications, 397:265–277, 2005. [5] Abdo Y. Alfakih, Amir Khandani, and Henry Wolkowicz. Solving Euclidean distance matrix completion problems via semidefinite programming. Computational Optimization and Applications, 12(1):13–30, January 1999. http://citeseer.ist.psu.edu/alfakih97solving.html [6] Abdo Y. Alfakih and Henry Wolkowicz. On the embeddability of weighted graphs in Euclidean spaces. Research Report CORR 98-12, Department of Combinatorics and Optimization, University of Waterloo, May 1998. http://citeseer.ist.psu.edu/alfakih98embeddability.html Erratum: p.390 herein. [7] Abdo Y. Alfakih and Henry Wolkowicz. Matrix completion problems. In Henry Wolkowicz, Romesh Saigal, and Lieven Vandenberghe, editors, Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, chapter 18. Kluwer, 2000. [8] Abdo Y. Alfakih and Henry Wolkowicz. Two theorems on Euclidean distance matrices and Gale transform. Linear Algebra and its Applications, 340:149–154, 2002. [9] Farid Alizadeh. Combinatorial Optimization with Interior Point Methods and Semi-Definite Matrices. PhD thesis, University of Minnesota, Computer Science Department, Minneapolis Minnesota USA, October 1991. 721
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- Page 723 and 724: BIBLIOGRAPHY 723 [24] Alexander I.
- Page 725 and 726: BIBLIOGRAPHY 725 [52] Stephen Boyd,
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- Page 731 and 732: BIBLIOGRAPHY 731 [132] Michel X. Go
- Page 733 and 734: BIBLIOGRAPHY 733 [162] T. Herrmann,
- Page 735 and 736: BIBLIOGRAPHY 735 [191] Mark Kahrs a
- Page 737 and 738: BIBLIOGRAPHY 737 [220] K. V. Mardia
- Page 739 and 740: BIBLIOGRAPHY 739 [250] Pythagoras P
- Page 741 and 742: BIBLIOGRAPHY 741 [277] Anthony Man-
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- Page 757 and 758: INDEX 757 of point, 37 ray, 90 rela
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- Page 765 and 766: INDEX 765 convex envelope, see conv
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- Page 769 and 770: INDEX 769 trilateration, 21, 42, 36
Bibliography<br />
[1] Suliman Al-Homidan and Henry Wolkowicz. Approximate and exact completion<br />
problems for Euclidean distance matrices using semidefinite programming, April<br />
2004.<br />
orion.math.uwaterloo.ca/∼hwolkowi/henry/reports/edmapr04.ps<br />
[2] Faiz A. Al-Khayyal and James E. Falk. Jointly constrained biconvex programming.<br />
Mathematics of Operations Research, 8(2):273–286, May 1983.<br />
http://www.convexoptimization.com/TOOLS/Falk.pdf<br />
[3] Abdo Y. Alfakih. On the uniqueness of Euclidean distance matrix completions.<br />
Linear Algebra and its Applications, 370:1–14, 2003.<br />
[4] Abdo Y. Alfakih. On the uniqueness of Euclidean distance matrix completions: the<br />
case of points in general position. Linear Algebra and its Applications, 397:265–277,<br />
2005.<br />
[5] Abdo Y. Alfakih, Amir Khandani, and Henry Wolkowicz. Solving Euclidean<br />
distance matrix completion problems via semidefinite programming. Computational<br />
<strong>Optimization</strong> and Applications, 12(1):13–30, January 1999.<br />
http://citeseer.ist.psu.edu/alfakih97solving.html<br />
[6] Abdo Y. Alfakih and Henry Wolkowicz. On the embeddability of weighted graphs<br />
in Euclidean spaces. Research Report CORR 98-12, Department of Combinatorics<br />
and <strong>Optimization</strong>, University of Waterloo, May 1998.<br />
http://citeseer.ist.psu.edu/alfakih98embeddability.html<br />
Erratum: p.390 herein.<br />
[7] Abdo Y. Alfakih and Henry Wolkowicz. Matrix completion problems. In<br />
Henry Wolkowicz, Romesh Saigal, and Lieven Vandenberghe, editors, Handbook<br />
of Semidefinite Programming: Theory, Algorithms, and Applications, chapter 18.<br />
Kluwer, 2000.<br />
[8] Abdo Y. Alfakih and Henry Wolkowicz. Two theorems on Euclidean distance<br />
matrices and Gale transform. Linear Algebra and its Applications, 340:149–154,<br />
2002.<br />
[9] Farid Alizadeh. Combinatorial <strong>Optimization</strong> with Interior Point Methods and<br />
Semi-Definite Matrices. PhD thesis, University of Minnesota, Computer Science<br />
Department, Minneapolis Minnesota USA, October 1991.<br />
721
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