This volume is intended for readers who are familiar with the basic approaches and methods of mathematical optimization. The subject matter is concerned with optimization problems in which some or all of the individual data involved depend on one parameter. This book considers thwe applications of solution algorithms for one-parameter optimization problems in the following fields: globally convergent algorithms for nonlinear, in particular non-convex, optimization problems, global optimization and multiobjective optimization. The main tool for a solution algorithm for a one-parametric optimization problem used is the so-called pathfollowing methods. Classical methods in the set of statianory points will be extended to the set of all generalized critical points. The book contains theoretical background information and introduces two generic classes. It also discusses the jump from one connected component in the set of local minimizers and generalized critical points to another one.
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Für höhere Schule und Studium
Für Beruf und Forschung
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60 line drawings, tables, index
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ISBN-13
978-0-471-92807-2 (9780471928072)
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Schweitzer Klassifikation
Part 1 Introduction: a preliminary survey on solution algorithms in one-parametric optimization; some motivations; abstracts of the chapters 2-6. Part 2 Theoretical background: unconstrained optimization problems; constraint sets; critical points, stationary points, stability; generic singularities in one-parametric optimization problems; the approach via piecewise differentiability. Part 3 Pathfollowing of curves of local minimizers: the estimation of the radius of convergence; an active index set strategy; the ALGORITHM PATH I and numerical results. Part 4 Pathfollowing along a connected component in the Karush-Kuhn-Tucker set and in the critical set: pathfollowing in the Karush-Kuhn-Tucker set; the ALGORITHM PATH II and numerical results; pathfollowing in the critical set; the ALGORITHM PATH III. Part 5 Pathfollowing in the set of local minimizers and in the set of critical points: jumps in the set of local minimizers and the ALGORITHM JUMP I; jumps in the critical set and the ALGORITHM JUMP II. Part 6 Applications: on globally convergent algorithms; on global optimization; on multiobjective optimization.
