Mixed Integer Nonlinear Programming
Sven Leyffer
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| Main Author: | |
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| Other Authors: | |
| Format: | Conference Paper |
| Language: | English |
| Published: |
New York, NY
Springer Science+Business Media, LLC
2012
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| Series: | The IMA Volumes in Mathematics and its Applications
154 |
| In: |
The IMA volumes in mathematics and its applications (154)
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| Volumes / Articles: | Show Volumes / Articles. |
| DOI: | 10.1007/978-1-4614-1927-3 |
| Subjects: | |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: http://dx.doi.org/10.1007/978-1-4614-1927-3 Verlag, Zentralblatt MATH, Inhaltstext: https://zbmath.org/?q=an:1230.90005 
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| Author Notes: | edited by Jon Lee, Sven Leyffer |
Table of Contents:
- Mixed Integer Nonlinear Programming; FOREWORD; PREFACE; CONTENTS; PART I: Convex MINLP; ALGORITHMS AND SOFTWARE FORCONVEX MIXED INTEGER NONLINEAR PROGRAMS; 1. Introduction.; 2. MINLP.; 2.1. MINLP problem classes.; 2.2. Basic elements of MINLP methods.; 3. Algorithms for convex MINLP.; 3.1. NLP-Based Branch and Bound.; 3.2. Outer Approximation.; 3.3. Generalized Benders Decomposition.; 3.4. Extended Cutting Plane.; 3.5. LP/NLP-Based Branch-and-Bound.; 4. Implementation techniques for convex MINLP.; 4.1. Linearization generation.; 4.2. Branching rules.; 4.2.1. Strong-branching.
- 4.2.2. Pseudo-costs.4.3. Node selection rules.; 4.4. Cutting planes.; 4.4.1. Gomory cuts.; 4.4.2. Mixed integer rounding.; 4.4.3. Disjunctive inequalities.; 4.5. Heuristics.; 4.5.1. Diving heuristics.; 4.5.2. Feasibility pumps.; 5. Software.; 5.1. ?-ECP; 5.2. Bonmin.; 5.3. DICOPT.; 5.4. FilMINT.; 5.5. MINLP BB.; 5.6. SBB.; 6. Computational study.; 6.1. Problems; 6.2. Computational results.; 7. Conclusions.; Acknowledgments.; SUBGRADIENT BASED OUTER APPROXIMATION FOR MIXED INTEGER SECOND ORDER CONE PROGRAMMING*; 1. Introduction.; 2. Preliminaries.; 3. Feasible nonlinear subproblems.
- 4. Infeasible nonlinear subproblems.5. The algorithm.; 6. Numerical experiments.; 7. Summary.; Acknowledgements.; PERSPECTIVE REFORMULATION AND APPLICATIONS; 1. Introduction.; 1.1. Motivation.; 1.2. The importance of formulation.; 1.3. The perspective reformulation.; 2. Perspective functions and convex hulls.; 2.1. Using perspective functions to obtain convex hulls.; 2.2. Computational challenges.; 3. Simple sets.; 3.1. The convex hull of a point and a convex set.; 3.2. The convex hull of a ray and a convex set.; 3.3. A simple quadratic set.; 3.4. A larger quadratic set.
- 3.5. A simple non-quadratic set.4. Applications.; 4.1. Separable Quadratic UFL.; 4.2. Network design with congestion constraints.; 4.3. Scheduling with controllable processing times.; 4.4. The unit commitment problem.; 4.5. Stochastic service system design.; 4.6. Portfolio selection.; 5. Computational approaches.; 5.1. NLP solvers.; 5.2. SOCP solvers.; 5.3. LP solvers.; 6. Computational results.; 6.1. Separable quadratic uncapacitated facility location.; 6.2. Stochastic service design.; 7. Conclusions.; Acknowledgments.; PART II: Disjunctive Programming
- GENERALIZED DISJUNCTIVE PROGRAMMING: A FRAMEWORK FOR FORMULATION AND ALTERNATIVE ALGORITHMS FOR MINLP OPTIMIZATION1. Introduction.; 2. Generalized disjunctive programming.; 2.1. Formulation.; 2.2. Illustrative example.; 2.3. Solution methods.; 2.3.1. MINLP reformulation; 2.3.2. Logic-Based Methods.; 2.3.3. Example.; 2.4. Special cases.; 2.4.1. Linear generalized disjunctive programming; 2.4.2. Nonconvex generalized disjunctive programs.; 3. Conclusions.; Aknowledgments.; DISJUNCTIVE CUTS FOR NONCONVEX MINLP; 1. Motivation: nonconvex MINLP.; 2. Lower bounds of an MINLP.
- 3. Disjunctions in MINLP.