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30
Complete search in continuous global optimization and constraint satisfaction, Acta Numerica 13
, 2004
"... A chapter for ..."
Review of nonlinear mixedinteger and disjunctive programming techniques
 Optimization and Engineering
, 2002
"... This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are ex ..."
Abstract

Cited by 55 (15 self)
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This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs : II. Application of Theory and Test Problems
 Engng
, 1990
"... In Part I (Floudas and Visweswaran, 1990), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the rigorous solution of the problem through a series of primal and relaxed dual problems until th ..."
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Cited by 53 (21 self)
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In Part I (Floudas and Visweswaran, 1990), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the rigorous solution of the problem through a series of primal and relaxed dual problems until the upper and lower bounds from these problems converged to an fflglobal optimum. In this paper, theoretical results are presented for several classes of mathematical programming problems that include : (i) the general quadratic programming problem, (ii) quadratic programming problems with quadratic constraints, (iii) pooling and blending problems, and (iv) unconstrained and constrained optimization problems with polynomial terms in the objective function and/or constraints. For each class, a few examples are presented illustrating the approach. Keywords : Global Optimization, Quadratic Programming, Quadratic Constraints, Polynomial functions, Pooling and Blending Problems. Author to whom...
Quadratic Optimization
, 1995
"... . Quadratic optimization comprises one of the most important areas of nonlinear programming. Numerous problems in real world applications, including problems in planning and scheduling, economies of scale, and engineering design, and control are naturally expressed as quadratic problems. Moreover, t ..."
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Cited by 45 (3 self)
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. Quadratic optimization comprises one of the most important areas of nonlinear programming. Numerous problems in real world applications, including problems in planning and scheduling, economies of scale, and engineering design, and control are naturally expressed as quadratic problems. Moreover, the quadratic problem is known to be NPhard, which makes this one of the most interesting and challenging class of optimization problems. In this chapter, we review various properties of the quadratic problem, and discuss different techniques for solving various classes of quadratic problems. Some of the more successful algorithms for solving the special cases of bound constrained and large scale quadratic problems are considered. Examples of various applications of quadratic programming are presented. A summary of the available computational results for the algorithms to solve the various classes of problems is presented. Key words: Quadratic optimization, bilinear programming, concave pro...
Global Optimization for the Phase Stability Problem
 AIChE J
, 1994
"... The Gibbs tangent plane criterion has become an important tool in determining the quality of obtained solutions to the phase and chemical equilibrium problem. The ability to determine if a postulated solution is thermodynamically stable with respect to perturbations in any or all of the phases is ve ..."
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Cited by 20 (4 self)
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The Gibbs tangent plane criterion has become an important tool in determining the quality of obtained solutions to the phase and chemical equilibrium problem. The ability to determine if a postulated solution is thermodynamically stable with respect to perturbations in any or all of the phases is very useful in the search for the true equilibrium solution. Previous approaches have concentrated on finding the stationary points of the tangent plane distance function. However, no guarantee of obtaining all stationary points can be provided. These difficulties arise due to the complex and nonlinear nature of the models used to predict equilibrium. In this work, simpler formulations for the stability problem are presented for the special class of problems where nonideal liquid phases can be adequately modeled using the NRTL and UNIQUAC activity coefficient equations. It is shown how the global minimum of the tangent plane distance function can be obtained for this class of problems. The adv...
Global Optimization And Analysis For The Gibbs Free Energy Function Using The Unifac, Wilson And Asog Equations
 I&EC Res
, 1994
"... The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomponent mixtures with only binary parameters, but was incapable of predicting more than one liquid phase. The UNIFAC and ASOG group contribution methods do not ha ..."
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Cited by 16 (5 self)
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The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomponent mixtures with only binary parameters, but was incapable of predicting more than one liquid phase. The UNIFAC and ASOG group contribution methods do not have this limitation and can predict the presence of multiple liquid phases. The most important area of application of all these equations is in the prediction of phase equilibrium. The calculation of phase equilibrium involves two important problems: (i) the minimization of the Gibbs free energy, and (ii) the tangent plane stability criterion. Problem (ii), which can be implemented as the minimization of the tangent plane distance function, has found wide application in aiding the search for the global minimum of the Gibbs free energy. However, a drawback of all previous approaches is that they could not provide theoretical guarantees that the true equilibrium solution will be obtained. The g...
Reformulations in Mathematical Programming: A Computational Approach
"... Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathema ..."
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Cited by 16 (12 self)
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Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathematical expressions of the parameters and decision variables, and therefore excludes optimization of blackbox functions. A reformulation of a mathematical program P is a mathematical program Q obtained from P via symbolic transformations applied to the sets of variables, objectives and constraints. We present a survey of existing reformulations interpreted along these lines, some example applications, and describe the implementation of a software framework for reformulation and optimization. 1
Global Optimization of MixedInteger Nonlinear Problems
 AIChE J
"... Two novel deterministic global optimization algorithms for nonconvex mixedinteger problems (MINLPs) are proposed, using the advances of the ffBB algorithm for nonconvex NLPs Adjiman et al. (1998a). The Special Structure MixedInteger ffBB algorithm (SMINffBB addresses problems with nonconvexities ..."
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Cited by 14 (2 self)
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Two novel deterministic global optimization algorithms for nonconvex mixedinteger problems (MINLPs) are proposed, using the advances of the ffBB algorithm for nonconvex NLPs Adjiman et al. (1998a). The Special Structure MixedInteger ffBB algorithm (SMINffBB addresses problems with nonconvexities in the continuous variables and linear and mixedbilinear participation of the binary variables. The General Structure MixedInteger ffBB algorithm (GMINffBB), is applicable to a very general class of problems for which the continuous relaxation is twice continuously differentiable. Both algorithms are developed using the concepts of branchandbound, but they differ in their approach to each of the required steps. The SMINffBB algorithm is based on the convex underestimation of the continuous functions while the GMINffBB algorithm is centered around the convex relaxation of the entire problem. Both algorithms rely on optimization or interval based variable bound updates to enhance effici...
Decomposition Based and Branch and Bound Global Optimization Approaches for the Phase Equilibrium Problem
 Journal of Global Optimization
, 1994
"... An increasingly popular approach when solving the phase and chemical equilibrium problem is to pose it as an optimization problem. However, difficulties are encountered due to the highly nonlinear nature of the models used to represent the behavior of the fluids, and because of the existence of mult ..."
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Cited by 12 (8 self)
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An increasingly popular approach when solving the phase and chemical equilibrium problem is to pose it as an optimization problem. However, difficulties are encountered due to the highly nonlinear nature of the models used to represent the behavior of the fluids, and because of the existence of multiple local solutions. This work shows how it is possible to guarantee fflglobal solutions for a certain important class of the phase and chemical equilibrium problem, namely when the liquid phase can be modeled using either the NonRandom TwoLiquid (NRTL) equation, or the UNIversal QUAsi Chemical (UNIQUAC) equation. Ideal vapor phases are easily incorporated into the global optimization framework. A number of interesting properties are described which drastically alter the structure of the respective problems. For the NRTL equation, it is shown that the formulation can be converted into a biconvex optimization problem. The GOP algorithm of Floudas and Visweswaran [8, 9] can then be used to...
Reformulation and Convex Relaxation Techniques for Global Optimization
 4OR
, 2004
"... Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested i ..."
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Cited by 9 (7 self)
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Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested in determining the globally optimal point. This thesis is concerned with techniques for establishing such global optima using spatial BranchandBound (sBB) algorithms.