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Mixed Integer Nonlinear Programming

  • Conference proceedings
  • © 2012

Overview

Editors:
  1. Jon Lee

    1. , College of Engineering, University of Michigan, Ann Arbor, USA

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  2. Sven Leyffer

    1. , Mathematics and Computer Science, Argonne National Laboratory, Argonne, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Contains expository and research papers based on a highly successful IMA Hot Topics Workshop “Mixed-Integer Nonlinear Optimization: Algorithmic Advances and Applications”
  • Combines the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables
  • Includes survey articles, new research material, and novel applications of MINLP

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 154)

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Table of contents (22 papers)

  1. Front Matter

    Pages i-xvii
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  2. Convex MINLP

    1. Front Matter

      Pages 1-1
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    2. Algorithms and Software for Convex Mixed Integer Nonlinear Programs

      • Pierre Bonami, Mustafa Kilinç, Jeff Linderoth
      Pages 1-39

    3. Subgradient Based Outer Approximation for Mixed Integer Second Order Cone Programming

      • Sarah Drewes, Stefan Ulbrich
      Pages 41-59

    4. Perspective Reformulation and Applications

      • Oktay Günlük, Jeff Linderoth
      Pages 61-89

  3. Disjunctive Programming

    1. Front Matter

      Pages 91-91
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    2. Generalized Disjunctive Programming: A Framework for Formulation and Alternative Algorithms for MINLP Optimization

      • Ignacio E. Grossmann, Juan P. Ruiz
      Pages 93-115

    3. Disjunctive Cuts for Nonconvex MINLP

      • Pietro Belotti
      Pages 117-144

  4. Nonlinear Programming

    1. Front Matter

      Pages 145-145
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    2. Sequential Quadratic Programming Methods

      • Philip E. Gill, Elizabeth Wong
      Pages 147-224

    3. Using Interior-Point Methods within an Outer Approximation Framework for Mixed Integer Nonlinear Programming

      • Hande Y. Benson
      Pages 225-243

  5. Expression Graphs

    1. Front Matter

      Pages 245-245
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    2. Using Expression Graphs in Optimization Algorithms

      • David M. Gay
      Pages 247-262

    3. Symmetry in Mathematical Programming

      • Leo Liberti
      Pages 263-283

  6. Convexification and Linearization

    1. Front Matter

      Pages 285-285
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    2. Using Piecewise Linear Functions for Solving MINLPs

      • Björn Geißler, Alexander Martin, Antonio Morsi, Lars Schewe
      Pages 287-314

    3. An Algorithmic Framework for MINLP with Separable Non-Convexity

      • Claudia D’Ambrosio, Jon Lee, Andreas Wächter
      Pages 315-347

    4. Global Optimization of Mixed-Integer Signomial Programming Problems

      • Andreas Lundell, Tapio Westerlund
      Pages 349-369

  7. Mixed-Integer Quadraticaly Constrained Optimization

    1. Front Matter

      Pages 371-371
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    2. The MILP Road to MIQCP

      • Samuel Burer, Anureet Saxena
      Pages 373-405
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Keywords

About this book

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.

Editors and Affiliations

  • , College of Engineering, University of Michigan, Ann Arbor, USA

    Jon Lee

  • , Mathematics and Computer Science, Argonne National Laboratory, Argonne, USA

    Sven Leyffer

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