Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

1. Front Matter

   Pages i-xxv

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2. Introduction

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 1-23

3. Convex Extensions and Relaxation Strategies

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 25-70

4. Product Disaggregation in Global Optimization and Relaxations of Rational Programs

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 71-123

5. Relaxations of Factorable Programs

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 125-145

6. Domain Reduction

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 147-187

7. Node Partitioning Schemes

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 189-211

8. The Implementation

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 213-228

9. Refrigerant Design Problem

   • Mohit Tawarmalani, Nikolaos V. Sahinidis

   Pages 229-252

10. The Pooling Problem

    • Mohit Tawarmalani, Nikolaos V. Sahinidis

    Pages 253-283

11. Miscellaneous Problems

    • Mohit Tawarmalani, Nikolaos V. Sahinidis

    Pages 285-312

12. GAMS/BARON: A Tutorial and Empirical Performance Analysis

    • Mohit Tawarmalani, Nikolaos V. Sahinidis

    Pages 313-401

13. Back Matter

    Pages 403-478

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Interest in constrained optimization originated with the simple linear pro­ gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re­ visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de­ velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter­ ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

• Partition
• algorithm
• algorithms
• global optimization
• linear optimization
• model
• nonlinear optimization
• operations research
• optimization
• programming
• data structures

• Purdue University, West Lafayette, USA

  Mohit Tawarmalani

• University of Illinois, Urbana, USA

  Nikolaos V. Sahinidis

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