Topics in semidefinite and interior-point methods
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Bibliographic Information
Topics in semidefinite and interior-point methods
（Fields Institute communications, v. 18）
American Mathematical Society, 1998
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
C-P||[Toronto]||[1997.9]200021326586
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Includes bibliographical references
Description and Table of Contents
Description
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.
Table of Contents
Theory: Optimality conditions and sensitivity analysis of cone-constrained and semi-definite programs by A. Shapiro Testing the feasibility of semidefinite programs by L. Porkolab and L. Khachiyan Polyhedra, spectrahedra, and semidefinite programming by M. V. Ramana Infinite-dimensional semidefinite programming: Regularized determinants and self-concordant barriers by L. Faybusovich Applications: A tour d'horizon on positive semidefinite and Euclidean distance matrix completion problems by M. Laurent Semidefinite programming and graph equipartition by S. E. Karisch and F. Rendl The totally nonnegative completion problem by C. R. Johnson, B. K. Kroschel, and M. Lundquist The multi-SAT algorithm by J. Gu How efficiently can we maximize threshold pseudo-Boolean functions? by M. R. Emamy-K. Faster algorithm for shortest network under given topology by G. Xue, D.-Z. Du, and F. K. Hwang Bayesian heuristic approach (BHA) and applications to discrete optimization by A. Mockus, J. Mockus, and L. Mockus Approximation clustering: A mine of semidefinite programming problems by B. Mirkin Algorithms: A long-step path following algorithm for semidefinite programming problems by K. M. Anstreicher and M. Fampa Cutting plane algorithms for semidefinite relaxations by C. Helmberg and R. Weismantel Infeasible-start semidefinite programming algorithms via self-dual embeddings by E. De Klerk, C. Roos, and T. Terlaky Solution of the trust region problem via a smooth unconstrained reformulation by S. Lucidi and L. Palagi.
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