Final report, DOE Grant DE-FG02-98ER25352, Computational semidefinite programming

Overton, Michael L.

Courant Institute of Mathematical Sciences, New York University, New York, NY (United States)

关键词: Linear Programming;    Vectors;    Cones;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Linear Programming;   

DOI  :  10.2172/806634
RP-ID  :  None
RP-ID  :  FG02-98ER25352
RP-ID  :  806634

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.