v2010.10.26 - Convex Optimization
v2010.10.26 - Convex Optimization v2010.10.26 - Convex Optimization
780 APPENDIX F. NOTATION AND A FEW DEFINITIONSK ◦ polar cone; K ∗ = −K ◦ , or angular degree as in 360 ◦K M+K MK λK ∗ λδHH −H +∂H∂H∂H −∂H +dmonotone nonnegative conemonotone conespectral conecone of majorizationhalfspacehalfspace described using an outward-normal (106) to the hyperplanepartially bounding ithalfspace described using an inward-normal (107) to the hyperplanepartially bounding ithyperplane; id est, partial boundary of halfspacesupporting hyperplanea supporting hyperplane having outward-normal with respect to set itsupportsa supporting hyperplane having inward-normal with respect to set itsupportsvector of distance-squared ijlower bound on distance-square d ijd ijABABCupper bound on distance-square d ijclosed line segment between points A and Bmatrix multiplication of A and Bclosure of set Cdecomposition orthonormal (1913) page 711, biorthogonal (1889) page 704expansion orthogonal (1923) page 713, biorthogonal (403) page 191
781vectorentrycubixquartixfeasible setsolution setoptimalfeasiblesameequivalentobjectiveprogramnatural ordercolumn vector in R nscalar element or real variable constituting a vector or matrixmember of R M×N×Lmember of R M×N×L×Kmost simply, the set of all variable values satisfying all constraints ofan optimization problemmost simply, the set of all optimal solutions to an optimization problem;a subset of the feasible set and not necessarily a single pointas in optimal solution, means solution to an optimization problem.optimal ⇒ feasibleas in feasible solution, means satisfies the (“subject to”) constraints ofan optimization problem, may or may not be optimalas in same problem, means optimal solution set for one problem isidentical to optimal solution set of another (without transformation)as in equivalent problem, means optimal solution to one problem can bederived from optimal solution to another via suitable transformationThe three objectives of Optimization are minimize, maximize, and findSemidefinite program is any convex minimization, maximization, orfeasibility problem constraining a variable to a subset of a positivesemidefinite cone.Prototypical semidefinite program conventionally means: a semidefiniteprogram having linear objective, affine equality constraints, but noinequality constraints except for cone membership. (4.1.1)Linear program is any feasibility problem, or minimization ormaximization of a linear objective, constraining the variable to anypolyhedron. (2.13.1.0.3)with reference to stacking columns in a vectorization means a vectormade from superposing column 1 on top of column 2 then superposingthe result on column 3 and so on; as in a vector made from entries of themain diagonal δ(A) means taken from left to right and top to bottom
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- Page 769 and 770: Appendix FNotation and a few defini
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- Page 787 and 788: Bibliography[1] Edwin A. Abbott. Fl
- Page 789 and 790: BIBLIOGRAPHY 789[23] Dror Baron, Mi
- Page 791 and 792: BIBLIOGRAPHY 791[49] Leonard M. Blu
- Page 793 and 794: BIBLIOGRAPHY 793[74] Yves Chabrilla
- Page 795 and 796: BIBLIOGRAPHY 795[102] Etienne de Kl
- Page 797 and 798: BIBLIOGRAPHY 797[129] Carl Eckart a
- Page 799 and 800: BIBLIOGRAPHY 799[154] James Gleik.
- Page 801 and 802: BIBLIOGRAPHY 801[182] Johan Håstad
- Page 803 and 804: BIBLIOGRAPHY 803[212] Viren Jain an
- Page 805 and 806: BIBLIOGRAPHY 805[237] Monique Laure
- Page 807 and 808: BIBLIOGRAPHY 807[265] Sunderarajan
- Page 809 and 810: BIBLIOGRAPHY 809Notes in Computer S
- Page 811 and 812: BIBLIOGRAPHY 811[319] Anthony Man-C
- Page 813 and 814: BIBLIOGRAPHY 813[346] Pham Dinh Tao
- Page 815 and 816: BIBLIOGRAPHY 815[375] Bernard Widro
- Page 817 and 818: Index∅, see empty set0-norm, 229,
- Page 819 and 820: INDEX 819bees, 30, 413Bellman, 276b
- Page 821 and 822: INDEX 821circular, 130construction,
- Page 823 and 824: INDEX 823measure, 295convex, 21, 36
- Page 825 and 826: INDEX 825duality, 160, 410gap, 161,
- Page 827 and 828: INDEX 827positive semidefinite, 284
- Page 829 and 830: INDEX 829point, 39, 62positive semi
780 APPENDIX F. NOTATION AND A FEW DEFINITIONSK ◦ polar cone; K ∗ = −K ◦ , or angular degree as in 360 ◦K M+K MK λK ∗ λδHH −H +∂H∂H∂H −∂H +dmonotone nonnegative conemonotone conespectral conecone of majorizationhalfspacehalfspace described using an outward-normal (106) to the hyperplanepartially bounding ithalfspace described using an inward-normal (107) to the hyperplanepartially bounding ithyperplane; id est, partial boundary of halfspacesupporting hyperplanea supporting hyperplane having outward-normal with respect to set itsupportsa supporting hyperplane having inward-normal with respect to set itsupportsvector of distance-squared ijlower bound on distance-square d ijd ijABABCupper bound on distance-square d ijclosed line segment between points A and Bmatrix multiplication of A and Bclosure of set Cdecomposition orthonormal (1913) page 711, biorthogonal (1889) page 704expansion orthogonal (1923) page 713, biorthogonal (403) page 191
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