teesid's optimization [5 articles]

Abstract

this paper. The link between the weak convergence and the epigraph convergence used in convex analysis is done. The Cramer transform used in the large deviation literature is defined as the composition of the Laplace transform by the logarithm by the Fenchel transform. It transforms convolution into inf-convolution. Probabilistic results about processes with independent increments are then transformed into similar results on dynamic programming equations. Cramer transform gives new insight on... ...

Abstract

. The problem of maximizing the determinant of a matrix subject to linear matrix inequalities (LMIs) arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical... ...

Abstract

Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics. ...

Abstract

This paper is a tutorial in a general and explicit procedure to simplify semidefinite programming problems which are invariant under the action of a group. The procedure is based on basic notions of representation theory of finite groups. As an example we derive the block diagonalization of the Terwilliger algebra in this framework. Here its connection to the orthogonal Hahn and Krawtchouk polynomials becomes visible. ...