v2007.09.13 - 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2875 Euclidean Distance Matrix 28973 Convex hull of three points . . . . . . . . . . . . . . . . . . . . 29074 Complete dimensionless EDM graph . . . . . . . . . . . . . . 29375 Fifth Euclidean metric property . . . . . . . . . . . . . . . . . 29576 Arbitrary hexagon in R 3 . . . . . . . . . . . . . . . . . . . . . 30477 Kissing number . . . . . . . . . . . . . . . . . . . . . . . . . . 30678 Trilateration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31079 This EDM graph provides unique isometric reconstruction . . 31480 Two sensors • and three anchors ◦ . . . . . . . . . . . . . . . 31481 Two discrete linear trajectories of sensors . . . . . . . . . . . . 31582 Coverage in cellular telephone network . . . . . . . . . . . . . 31883 Contours of equal signal power . . . . . . . . . . . . . . . . . . 31884 Example of molecular conformation . . . . . . . . . . . . . . . 32085 Orthogonal complements in S N abstractly oriented . . . . . . . 33086 Elliptope E 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34987 Elliptope E 2 interior to S 2 + . . . . . . . . . . . . . . . . . . . . 35088 Smallest eigenvalue of −VN TDV N . . . . . . . . . . . . . . . . 35589 Some entrywise EDM compositions . . . . . . . . . . . . . . . 35590 Map of United States of America . . . . . . . . . . . . . . . . 36991 Largest ten eigenvalues of −VN TOV N . . . . . . . . . . . . . . 372