v2006.03.09 - Convex Optimization

30 LIST OF FIGURES6 Semidefinite programming 35388 Visualizing positive semidefinite cone in high dimension . . . . 3577 EDM proximity 38789 Pseudo-Venn diagram . . . . . . . . . . . . . . . . . . . . . . 39090 Elbow placed in path of projection . . . . . . . . . . . . . . . 391A Linear algebra 42391 Geometrical interpretation of full SVD . . . . . . . . . . . . . 454B Simple matrices 46192 Four fundamental subspaces of any dyad . . . . . . . . . . . . 46393 Four fundamental subspaces of a doublet . . . . . . . . . . . . 46794 Four fundamental subspaces of elementary matrix . . . . . . . 46895 Gimbal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476D Matrix calculus 49596 Convex quadratic bowl in R 2 × R . . . . . . . . . . . . . . . . 505E Projection 52397 Nonorthogonal projection of x∈ R 3 on R(U)= R 2 . . . . . . . 52898 Biorthogonal expansion of point x∈aff K . . . . . . . . . . . . 53999 Dual interpretation of projection on convex set . . . . . . . . . 558100 Projection product on convex set in subspace . . . . . . . . . 566101 von Neumann-style projection of point b . . . . . . . . . . . . 569102 Alternating projection on two halfspaces . . . . . . . . . . . . 570103 Distance, optimization, feasibility . . . . . . . . . . . . . . . . 572104 Alternating projection on nonnegative orthant and hyperplane 575105 Geometric convergence of iterates in norm . . . . . . . . . . . 575106 Distance between PSD cone and iterate in A . . . . . . . . . . 579107 Dykstra’s alternating projection algorithm . . . . . . . . . . . 581108 Normal cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582