v2007.09.17 - Convex Optimization

LIST OF FIGURES 1559 Quadratic function convexity in terms of its gradient . . . . . 20860 Plausible contour plot . . . . . . . . . . . . . . . . . . . . . . 21261 Iconic quasiconvex function . . . . . . . . . . . . . . . . . . . 2204 Semidefinite programming 22562 Visualizing positive semidefinite cone in high dimension . . . . 22963 2-lattice of sensors and anchors for localization example . . . . 26164 3-lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26265 4-lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26366 5-lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26467 ellipsoids of orientation and eccentricity . . . . . . . . . . . . . 26568 a 2-lattice solution for localization . . . . . . . . . . . . . . . . 27069 a 3-lattice solution . . . . . . . . . . . . . . . . . . . . . . . . 27070 a 4-lattice solution . . . . . . . . . . . . . . . . . . . . . . . . 27171 a 5-lattice solution . . . . . . . . . . . . . . . . . . . . . . . . 27172 MIT logo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28773 One-pixel camera . . . . . . . . . . . . . . . . . . . . . . . . . 2885 Euclidean Distance Matrix 29174 Convex hull of three points . . . . . . . . . . . . . . . . . . . . 29275 Complete dimensionless EDM graph . . . . . . . . . . . . . . 29576 Fifth Euclidean metric property . . . . . . . . . . . . . . . . . 29777 Arbitrary hexagon in R 3 . . . . . . . . . . . . . . . . . . . . . 30678 Kissing number . . . . . . . . . . . . . . . . . . . . . . . . . . 30879 Trilateration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31280 This EDM graph provides unique isometric reconstruction . . 31681 Two sensors • and three anchors ◦ . . . . . . . . . . . . . . . 31682 Two discrete linear trajectories of sensors . . . . . . . . . . . . 31783 Coverage in cellular telephone network . . . . . . . . . . . . . 32084 Contours of equal signal power . . . . . . . . . . . . . . . . . . 32085 Example of molecular conformation . . . . . . . . . . . . . . . 32286 Orthogonal complements in S N abstractly oriented . . . . . . . 33287 Elliptope E 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35188 Elliptope E 2 interior to S 2 + . . . . . . . . . . . . . . . . . . . . 35289 Smallest eigenvalue of −VN TDV N . . . . . . . . . . . . . . . . 35790 Some entrywise EDM compositions . . . . . . . . . . . . . . . 35791 Map of United States of America . . . . . . . . . . . . . . . . 371