Semidefinite Programming

9:15 AM-10:00 AM

*Room: Capitol North/Center*

Chair: Adrian S. Lewis, University of Waterloo, Canada

Semidefinite programming (SDP) is an extension of linear programming, with real symmetric matrices replacing vector variables and positive semidefinite constraints replacing component wise inequalities. Interior-point methods are now routinely used to solve SDPs, or more generally self-dual convex cone programs, including quadratic cone constraints as well as semidefinite ones. Such problems arise in many applications, especially in robust control theory, where SDP constraints are known as LMI's: linear matrix inequalities.

The speaker will give a short history of the subject, discuss optimality conditions and related feasibility and degeneracy issues, outline some primal-dual interior-point algorithms, and survey the various software packages announced in recent years. He will discuss the outlook for solving large-scale SDP's, and report some recent efforts to solve large SDP's arising in quantum chemistry calculations.

**Michael L. Overton**

*Courant Institute of Mathematical Sciences*

*New York University*

*MMD, 12/17/98*