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Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography.
Audience: The book is intended for students, researchers and practitioners with a background in operations research, mathematics, mathematical programming, or statistics.
Inhaltsverzeichnis
1 Introduction.- 2 The Theory of Linear Programming.- 3 Sensitivity Analysis in Linear Programming.- 4 Sensitivity Analysis in Quadratic Programming.- 5 Primal-Dual Affine Scaling Methods for Linear Problems.- 6 Primal-Dual Affine Scaling Methods for Nonlinear Problems.- 7 Computational Results with Affine Scaling Methods.- 8 Target-Following for Linear Programming.- 9 Target-Follow [Ng for Nonlinear Programming.- 10 Semidefinite Programming.- 11. Interior Point Methods in Decomposition.- A Technical Results.- References.
