(See MS56 for Part II)
10:30 AM-12:00 PM
Room: Capitol South
Optimization problems involving (positive or negative) semidefinite and convex quadratic constraints have been subjects of intense study in the past several years. Interior point algorithms have been extended from linear programming to such optimization problems quite successfully so that nowadays, fairly large problems with semidefinite and convex quadratic constraints can be solved efficiently and with great numerical accuracy. Even more exciting is the sheer number and broad diversity of areas which use such optimization problems as models. Semidefinite programming and convex quadratically constrained programming arise as powerful modeling tools for a wide range of applications including, for example minimization of the largest eigenvalue of an affine set of matrices, calculation of sharp bounds on NP-hard combinatorial and integer programming problems, estimation of probability distribution of random variables with known moments, design of antenna arrays, estimation of parameters of feedback control systems, and design of efficient portfolios. In this two-part minisymposium the speakers present their latest results on solving problems with semidefinite and convex quadratic constraints in areas ranging over robust filtering, finance, statistics, combinatorial optimization, and truss topology.
Organizers: Farid Alizadeh
Rutgers University
Lieven Vandenberghe
University of California, Los Angeles
tjf, 1/19/99, MMD, 1/27/99