Description |
1 online resource (323 p.) |
Series |
Wiley Series in Operations Research and Management Science Ser |
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Wiley Series in Operations Research and Management Science Ser
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Contents |
Cover -- Title Page -- Copyright -- Contents -- Short Bios of the Authors -- Preface -- Chapter 1 Introduction -- 1.1 Concepts of Optimization -- 1.1.1 Convex Analysis -- 1.1.1.1 Properties of Convex Sets -- 1.1.1.2 Properties of Convex Functions -- 1.1.2 Optimality Conditions -- 1.1.2.1 Karush-Kuhn-Tucker Necessary Optimality Conditions -- 1.1.2.2 Karun-Kush-Tucker First-Order Sufficient Optimality Conditions -- 1.1.3 Interpretation of Lagrange Multipliers -- 1.2 Concepts of Multi-parametric Programming -- 1.2.1 Basic Sensitivity Theorem -- 1.3 Polytopes |
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1.3.1 Approaches for the Removal of Redundant Constraints -- 1.3.1.1 Lower-Upper Bound Classification -- 1.3.1.2 Solution of Linear Programming Problem -- 1.3.2 Projections -- 1.3.3 Modeling of the Union of Polytopes -- 1.4 Organization of the Book -- References -- Part I Multi-parametric Optimization -- Chapter 2 Multi-parametric Linear Programming -- 2.1 Solution Properties -- 2.1.1 Local Properties -- 2.1.2 Global Properties -- 2.2 Degeneracy -- 2.2.1 Primal Degeneracy -- 2.2.2 Dual Degeneracy -- 2.2.3 Connections Between Degeneracy and Optimality Conditions -- 2.3 Critical Region Definition |
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2.4 An Example: Chicago to Topeka -- 2.4.1 The Deterministic Solution -- 2.4.2 Considering Demand Uncertainty -- 2.4.3 Interpretation of the Results -- 2.5 Literature Review -- References -- Chapter 3 Multi-Parametric Quadratic Programming -- 3.1 Calculation of the Parametric Solution -- 3.1.1 Solution via the Basic Sensitivity Theorem -- 3.1.2 Solution via the Parametric Solution of the KKT Conditions -- 3.2 Solution Properties -- 3.2.1 Local Properties -- 3.2.2 Global Properties -- 3.2.3 Structural Analysis of the Parametric Solution -- 3.3 Chicago to Topeka with Quadratic Distance Cost |
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Chapter 5 Multi-parametric Mixed-integer Linear Programming -- 5.1 Solution Properties -- 5.1.1 From mp-LP to mp-MILP Problems -- 5.1.2 The Properties -- 5.2 Comparing the Solutions from Different mp-LP Problems -- 5.2.1 Identification of Overlapping Critical Regions -- 5.2.2 Performing the Comparison -- 5.2.3 Constraint Reversal for Coverage of Parameter Space -- 5.3 Multi-parametric Integer Linear Programming -- 5.4 Chicago to Topeka Featuring a Purchase Decision -- 5.4.1 Interpretation of the Results -- 5.5 Literature Review -- References |
Notes |
Description based upon print version of record |
Form |
Electronic book
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Author |
Diangelakis, Nikolaos A
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Oberdieck, Richard
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ISBN |
9781119265153 |
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1119265150 |
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