Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
Theory, Algorithms, Software, and Applications
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Nikolaos V. Sahinidis
Mathematical Modeling and Industrial Mathematics
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Reference Work Entry In depth
Chemical Process Planning
Keywords
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Reference Work Entry In depth
Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data
Introduction
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Reference Work Entry In depth
Contact Map Overlap Maximization Problem, CMO
Introduction
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Reference Work Entry In depth
Time-Dependent Traveling Salesman Problem
Keywords
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Book
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Chapter
Introduction
Research in optimization attracted attention when significant advances were made in linear programming—the optimization of a linear objective over a linear constraint set—in the late 1940s. The focus of the op...
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Chapter
The Implementation
BARON (Sahinidis 1996, Ghildyal & Sahinidis 2001, Sahinidis 1999–2000, Tawarmalani & Sahinidis 1999b, Sahinidis & Tawarmalani 2000), the branchand-reduce optimization navigator, includes an implementation of m...
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Chapter
Relaxations of Factorable Programs
In Chapter 2, we developed a theory of convex extensions and formalized a technique for building tight relaxations. However, the size of the resulting relaxations can be exponential in the number of variables....
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Node Partitioning Schemes
In this chapter, we concentrate on branching strategies for mixed-integer nonlinear programs. We introduce the notion of an ideal violation and use it to develop a partitioning technique for factorable program...
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Refrigerant Design Problem
The enumeration of large, combinatorial search spaces presents a central conceptual difficulty in molecular design. To address this difficulty, we develop an algorithm which guarantees globally optimal solutio...
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Chapter
Miscellaneous Problems
In this chapter, we provide computational experience with BARON on a variety of factorable nonlinear programs, including separable concave quadratic programs, indefinite quadratic programs, linear multiplicati...
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Product Disaggregation in Global Optimization and Relaxations of Rational Programs
In this chapter, we consider the product of a single continuous variable and the sum of a number of continuous variables. We show that “product disaggregation” (distributing the product over the sum) leads to ...
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Chapter
Domain Reduction
Domain reduction is the process of eliminating regions from the feasible space if the removal does not affect the convergence of the search process to a global optimum. Domain reduction is also referred to as ...
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The Pooling Problem
Convexification techniques based on disjunctive programming have been extensively employed to solve many hard combinatorial optimization problems. In this chapter, we demonstrate the potential of convexificati...
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GAMS/BARON: A Tutorial and Empirical Performance Analysis
The purpose of this chapter is threefold. First, to provide modelers, students, and practitioners with easily accessible models and reproducible computational results. Second, to demonstrate that the algorithm...
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Chapter
Convex Extensions and Relaxation Strategies
Central to the efficiency of global optimization methods for nonconvex mathematical programs is the capability to construct tight convex relaxations. In this chapter, we develop the theory of convex extensions...
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Reference Work Entry In depth
Time-Dependent Traveling Salesman Problem
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Reference Work Entry In depth
Chemical Process Planning
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Chapter
Solving Global Optimization Problems with Baron
The purpose of this paper is to report our progress to date towards the development of a general purpose global optimization system. The system has evolved from a 1800 line code initially written in the GAMS m...
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Chapter
A Finite Algorithm for Global Minimization of Separable Concave Programs
Researchers first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches nonlinear programming to be explored. This paper proposes a new finite...
