Abstract
Semidefinite programming (SDP) is an extension of linear programming, with vector variables replaced by matrix variables and component wise nonnegativity replaced by positive semidefiniteness. SDP's are convex, but not polyhedral, optimization problems. SDP is well on its way to becoming an established paradigm in optimization, with many current potential applications. Consequently, efficient methods and software for solving SDP's are of great importance. During the award period, attention was primarily focused on three aspects of computational semidefinite programming: General-purpose methods for semidefinite and quadratic cone programming; Specific applications (LMI problems arising in control, minimizing a sum of Euclidean norms, a quantum mechanics application of SDP); and Optimizing matrix stability.
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