MIT Department of Electrical Engineering & Computer Science
Optimization over Linear Matrix Inequalities
Dr. Lieven Vandenberghe
Stanford University
Thursday, April 4, 1996
4:15 PM (4:00 refreshments)
Grier Room, 34-401A
EECS Special Seminar
Abstract
Many nonlinear convex optimization problems can be cast as problems
involving linear matrix inequalities, and hence efficiently solved
using recently developed interior-point methods.
We will consider two specific problems:
- The semidefinite programming problem, i.e., the problem of minimizing
a linear cost function subject to a linear matrix inequality.
Semidefinite programming is an important numerical tool for analysis
and synthesis in systems and control theory. It has also been
recognized in combinatorial optimization as a valuable technique
for obtaining bounds on the solution of NP-hard problems.
- The problem of maximizing the determinant of a positive definite
matrix subject to linear matrix inequalities. This problem has
applications in computational geometry, experiment design,
information and communication theory, and other fields.
We will review some of these applications, including some interesting
applications that are less well known and arise in statistics, optimal
experiment design, and transistor sizing. We will then present an
efficient path-following interior-point method for both the
semidefinite programming and the determinant maximization problem,
and give a simplified analysis of the worst-case complexity.
URL of this page:
http://www-eecs.mit.edu/AY95-96/events/28.html
Created: Mar 7, 1996
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Modified: Jun 25, 1997
This announcement is from the MIT EECS 1995-96 archive.
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