EE 227 A / STAT 260 : Nonlinear and Convex Optimization Fall 2004 Lecture 4 — 9 Sep 2004

Convex Optimization Lecture Notes for EE 227 BT Draft , Fall 2013 Laurent

EE 227 A : Convex Optimization and Applications February 21 , 2012 Lecture 11 : SDP Duality

to represent the positive semi-definiteness condition X 0 in the SDP. The proof of the above representation of the minimum eigenvalue can be obtained by first showing that we can without loss of generality assume that A is diagonal, and noticing that we can then restrict Y to be diagonal as well. Note that the above representation proves that λmin is concave, so problem (11.2) is indeed convex ...

EE 227 A : Convex Optimization and Applications October 14 , 2008 Lecture 13 : SDP Duality

to represent the positive semi-definiteness condition X # 0 in the SDP. The proof of the above representation of the minimum eigenvalue can be obtained by first showing that we can without loss of generality assume that A is diagonal, and noticing that we can then restrict Y to be diagonal as well. Note that the above representation proves that λmin is concave, so problem (13.2) is indeed conve...

DS - GA 3001 . 03 : Extended Syllabus Lecture 10 Optimization and Computational Linear Algebra for Data Science ( Fall 2016 )

[1] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [2] Carlos Fernandez-Granda, Lecture Notes of “Optimization-based Data Analysis”, available at http: //www.cims.nyu.edu/~cfgranda/pages/OBDA_spring16/notes.html, 2016. [3] Carlos Fernandez-Granda, Lecture Notes of DSGA1002, available at http://www.cims.nyu.edu/ ~cfgranda/pages/DSGA1002_fall15/notes.html, 201...

An Introduction to Convexity

Contents 1 The basic concepts 1 1.1 Is convexity useful? 1 1.2 Nonnegative vectors 4 1.3 Linear programming 5 1.4 Convex sets, cones and polyhedra 6 1.5 Linear algebra and affine sets 11 1.6 Exercises 14 2 Convex hulls and Carathéodory's theorem 17 2.1 Convex and nonnegative combinations 17 2.2 The convex hull 19 2.3 Affine independence and dimension 22 2.4 Convex sets and topology 24 2.5 Carat...