Parametric Integer Optimization - Mandel, Reinhard

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Résumé :
Frontmatter -- Preface -- Contents -- 1. Introduction -- 2. Multifunctions and Constraint Sets -- 2.1. Definitions -- 2.2. Parameter Depending Constraint Sets -- 3. Stability of Some Continuous Optimization Problems -- 3.1. Definitions -- 3.2. Stability Properties -- 4. Quasiconvex Polynomial Optimization Problems -- 4.1. Properties of Quasiconvex Polynomial Functions -- 4.2. Multifunctions and Constraint Sets Defined by Quasi- convex Polynomial Functions -- 4.3. Stability Properties for a Fixed Objective Function -- 5. Integer Points in Certain Subsets of the Space Rn -- 5.1. Subsets Described as the Sum of a Compact Set and a Convex Cone -- 5.2. Subsets Described by Quasiconvex Polynomial Functions -- 5.3. Polyhedral Subsets -- 6. Stability Properties of Nonlinear Integer Optimization Problems -- 6.1. Introduction -- 6.2. Integer Problems with Quadratic Objective Function -- 6.3. Integer Problems with a Convex Polynomial Objective Function -- 7. The Existence of Optimal Points for Integer Optimization Problems -- 7.1. Concave Objective Functions -- 7.2. Polynomial Objective Functions -- 7.3. Some Special Mixed-Integer Optimization Problems -- 8. Quantitative Stability of (Mixed-) Integer Linear Optimization Problems -- 9. On Relations between Parametric Optimization, Solution Concepts and Subadditive Duality for Integer Optimization -- 9.1. Penalty Functions for (Mixed-) Integer Linear Optimization -- 9.2. Partitioning Procedures -- 9.3. Subadditive Duality -- Bibliography -- Backmatter...

Sommaire:
Frontmatter -- Preface -- Contents -- 1. Introduction -- 2. Multifunctions and Constraint Sets -- 2.1. Definitions -- 2.2. Parameter Depending Constraint Sets -- 3. Stability of Some Continuous Optimization Problems -- 3.1. Definitions -- 3.2. Stability Properties -- 4. Quasiconvex Polynomial Optimization Problems -- 4.1. Properties of Quasiconvex Polynomial Functions -- 4.2. Multifunctions and Constraint Sets Defined by Quasi- convex Polynomial Functions -- 4.3. Stability Properties for a Fixed Objective Function -- 5. Integer Points in Certain Subsets of the Space Rn -- 5.1. Subsets Described as the Sum of a Compact Set and a Convex Cone -- 5.2. Subsets Described by Quasiconvex Polynomial Functions -- 5.3. Polyhedral Subsets -- 6. Stability Properties of Nonlinear Integer Optimization Problems -- 6.1. Introduction -- 6.2. Integer Problems with Quadratic Objective Function -- 6.3. Integer Problems with a Convex Polynomial Objective Function -- 7. The Existence of Optimal Points for Integer Optimization Problems -- 7.1. Concave Objective Functions -- 7.2. Polynomial Objective Functions -- 7.3. Some Special Mixed-Integer Optimization Problems -- 8. Quantitative Stability of (Mixed-) Integer Linear Optimization Problems -- 9. On Relations between Parametric Optimization, Solution Concepts and Subadditive Duality for Integer Optimization -- 9.1. Penalty Functions for (Mixed-) Integer Linear Optimization -- 9.2. Partitioning Procedures -- 9.3. Subadditive Duality -- Bibliography -- Backmatter