Beschreibung
InhaltsangabeUnconstrained Problems.- General Introduction.- Basic Methods.- Line-Searches.- Newtonian Methods.- Conjugate Gradient.- Special Methods.- A Case Study: Seismic Reection Tomography.- Nonsmooth Optimization.- to Nonsmooth Optimization.- Some Methods in Nonsmooth Optimization.- Bundle Methods. The Quest for Descent.- Applications of Nonsmooth Optimization.- Computational Exercises.- Newton's Methods in Constrained Optimization.- Background.- Local Methods for Problems with Equality Constraints.- Local Methods for Problems with Equality and InequalityConstraints.- Exact Penalization.- Globalization by Line-Search.- Quasi-Newton Versions.- Interior-Point Algorithms for Linear and QuadraticOptimization.- Linearly Constrained Optimization and SimplexAlgorithm.- Linear Monotone Complementarity and Associated Vector Fields.- Predictor-Corrector Algorithms.- Non-Feasible Algorithms.- Self-Duality.- One-Step Methods.- Complexity of Linear Optimization Problems with Integer Data.- Karmarkar's Algorithm.
Inhaltsverzeichnis
General Introduction.- Part I: Unconstraint Problems: Basic Methods; Line-Searches; Newtonian Methods; Conjugate Gradient; Special Methods.- Part II: Nonsmooth Optimization: Some Theory of Nonsmooth Optimization; Some Methods in Nonsmooth Optimization; Bundle Methods. The Quest of Decent; Decomposition and Duality.- Part III: Newton''s Methods in Constrained Optimization: Background; Local Methods for Problems with Equality Constraints; Local Methods for Problems with Equality and Inequality Constraints; Exact Penalization; Globalization by Line-Search; Quasi-Newton Versions.- Part IV: Interior-Point Algorithms for Linear and Quadratic Optimization: Linearly Constrained Optimization and Simplex Algorithm; Linear Monotone Complementary and Associated Vector Fields; Predictor-Corrector Algorithms; Non-Feasible Algorithms; Self-Duality; One-Step Methods; Complexity of Linear Optimization Problems with Integer Data; Karmarkar''s Algorithm.- References.- Index.
Autorenporträt
The four authors are leading international specialists in various branches of nonlinear optimization (one of them received the Dantzig Prize). They are working - or have worked - at INRIA, the French National Institute for Research in Computer Science and Control, and they also teach in various universities and "Grandes Écoles". All of them continually collaborate with industry on problems dealing with optimization, in fields such as energy management, geoscience, life sciences, etc.
