v2007.09.17 - Convex Optimization

14 LIST OF FIGURES24 Nonconvex cone is convex cone boundary . . . . . . . . . . . . 8325 Cone exterior is convex cone . . . . . . . . . . . . . . . . . . . 8326 Truncated nonconvex cone X . . . . . . . . . . . . . . . . . . 8427 Not a cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8528 Minimum element. Minimal element. . . . . . . . . . . . . . . 8829 K is a pointed polyhedral cone having empty interior . . . . . 9230 Exposed and extreme directions . . . . . . . . . . . . . . . . . 9631 Positive semidefinite cone . . . . . . . . . . . . . . . . . . . . 9932 Convex Schur-form set . . . . . . . . . . . . . . . . . . . . . . 10133 Projection of the PSD cone . . . . . . . . . . . . . . . . . . . 10434 Circular cone showing axis of revolution . . . . . . . . . . . . 10935 Circular section . . . . . . . . . . . . . . . . . . . . . . . . . . 11136 Polyhedral inscription . . . . . . . . . . . . . . . . . . . . . . 11237 Conically (in)dependent vectors . . . . . . . . . . . . . . . . . 12138 Pointed six-faceted polyhedral cone and its dual . . . . . . . . 12339 Minimal set of generators for halfspace about origin . . . . . . 12540 Unit simplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13041 Two views of a simplicial cone and its dual . . . . . . . . . . . 13242 Two equivalent constructions of dual cone . . . . . . . . . . . 13643 Dual polyhedral cone construction by right angle . . . . . . . 13744 K is a halfspace about the origin . . . . . . . . . . . . . . . . 13845 Iconic primal and dual objective functions. . . . . . . . . . . . 13946 Orthogonal cones . . . . . . . . . . . . . . . . . . . . . . . . . 14347 Blades K and K ∗ . . . . . . . . . . . . . . . . . . . . . . . . . 14548 Shrouded polyhedral cone . . . . . . . . . . . . . . . . . . . . 15549 Simplicial cone K in R 2 and its dual . . . . . . . . . . . . . . . 16050 Monotone nonnegative cone K M+ and its dual . . . . . . . . . 17051 Monotone cone K M and its dual . . . . . . . . . . . . . . . . . 17252 Two views of monotone cone K M and its dual . . . . . . . . . 17353 First-order optimality condition . . . . . . . . . . . . . . . . . 1763 Geometry of convex functions 18354 Convex functions having unique minimizer . . . . . . . . . . . 18555 Affine function . . . . . . . . . . . . . . . . . . . . . . . . . . 19356 Supremum of affine functions . . . . . . . . . . . . . . . . . . 19557 Epigraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19558 Gradient in R 2 evaluated on grid . . . . . . . . . . . . . . . . 203