Convex Optimization

Published on Aug 26, 200741312 Views

Lieven Vandenberghe

The lectures will provide an introduction to the theory and applications of convex optimization. ;The emphasis will be on results useful for convex modeling, i.e., recognizing and formulating conve

MLSS 2007 - Tübingen

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Operations Research

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Chapter list

Convex optimization: Modeling and applications00:00

Outline00:35

Lecture 101:18

Introduction01:21

Mathematical optimization01:25

Least squares03:33

Linear programming05:34

Convex optimization problem-part0107:34

Convex optimization problem-part0208:22

History09:56

New applications since 199011:57

Interior-point methods12:52

Convex sets14:13

Definition14:22

Convex sets - A15:21

Hyperplanes and halfspaces15:48

Euclidean balls and ellipsoids16:31

Norm balls and norm cones17:22

Polyhedra18:41

Positive semidefinite cone19:25

Operations that preserve convexity21:04

Intersection21:24

Affine function24:39

Norm balls and norm cones - A27:07

Affine function - A27:16

Prospective and linear fractional function27:47

Example28:41

Convex functions32:21

Definition32:47

Examples on R33:40

Examples R and R34:21

Differentiable convex functions37:09

Examples39:31

Operations that preserve convexity41:25

Positive weighted sum and composition with affine function41:57

Pointwise maximum43:26

Pointwise supremum45:41