Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
Theory, Algorithms, Software, and Applications
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Nikolaos V. Sahinidis
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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...
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Chapter
Planning of Chemical Process Networks via Global Concave Minimization
The problem of selecting processes and planning expansions of a chemical complex to maximize net present value has been traditionally formulated as a multiperiod, mixed-integer linear program. In this paper, t...
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Article
BARON: A general purpose global optimization software package
The Branch-And-Reduce Optimization Navigator (BARON) is a computational system for facilitating the solution of nonconvex optimization problems to global optimality. We provide a brief description of the algor...
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A branch-and-reduce approach to global optimization
This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of the...
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Article
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 of nonlinear programming to be explored. This paper proposes a new alg...
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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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Analysis of Bounds for Multilinear Functions
We analyze four bounding schemes for multilinear functions and theoretically compare their tightness. We prove that one of the four schemes provides the convex envelope and that two schemes provide the concave...
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Article
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
In a recent work, we introduced the concept of convex extensions for lower semi-continuous functions and studied their properties. In this work, we present new techniques for constructing convex and concave en...
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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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Chapter
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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Chapter
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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Chapter
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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Chapter
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...
