Topics in Semidefinite and Interior-Point Methods

This volume contains refereed papers presented at the workshop on "Semidefinite Programming and Interior-Point Approaches for Combinatorial Optimization Problems" held at The Fields Institute in May 1996. Semidefinite programming (SDP) is a generalization of linear programming (LP) in that the nonnegativity constraints on the variables are replaced by a positive semidefinite constraint on matrix variables. Many of the elegant theoretical properties and powerful solution techniques follow through from LP to SDP. In particular, the primal-dual interior-point methods, which are currently so successful for LP, can be used to efficiently solve SDP problems.In addition to the interesting theoretical and algorithmic questions, SDP has found many important applications in combinatorial optimization, control theory and other areas of mathematical programming. SDP is currently a very hot area of research. The papers in this volume cover a wide spectrum of recent developments in SDP. The volume would be suitable as a textbook for advanced courses in optimization.