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Feasibilitybased bounds tightening via fixed points
, 2010
"... The search tree size of the spatial BranchandBound algorithm for MixedInteger Nonlinear Programming depends on many factors, one of which is the width of the variable ranges at every tree node. A range reduction technique often employed is called Feasibility Based Bounds Tightening, which is kn ..."
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Cited by 4 (2 self)
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The search tree size of the spatial BranchandBound algorithm for MixedInteger Nonlinear Programming depends on many factors, one of which is the width of the variable ranges at every tree node. A range reduction technique often employed is called Feasibility Based Bounds Tightening, which is known to be practically fast, and is thus deployed at every node of the search tree. From time to time, however, this technique fails to converge to its limit point in finite time, thereby slowing the whole BranchandBound search considerably. In this paper we propose a polynomial time method, based on solving a linear program, for computing the limit point of the Feasibility Based Bounds Tightening algorithm applied to linear equality and inequality constraints.
Strong formulations for convex functions over nonconvex sets, Optimization Online
, 2011
"... Abstract In this paper we derive strong linear inequalities for sets of the form where Q(x) : R d → R is a quadratic function, P ⊂ R d and "int" denotes interior. Of particular but not exclusive interest is the case where P denotes a closed convex set. In this paper, we present several ca ..."
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Abstract In this paper we derive strong linear inequalities for sets of the form where Q(x) : R d → R is a quadratic function, P ⊂ R d and "int" denotes interior. Of particular but not exclusive interest is the case where P denotes a closed convex set. In this paper, we present several cases where it is possible to characterize the convex hull by efficiently separable linear inequalities.
The ReformulationOptimization Software Engine
"... Most optimization software performs numerical computation, in the sense that the main interest is to find numerical values to assign to the decision variables, e.g. a solution to an optimization problem. In mathematical programming, however, a considerable amount of symbolic transformation is essen ..."
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Most optimization software performs numerical computation, in the sense that the main interest is to find numerical values to assign to the decision variables, e.g. a solution to an optimization problem. In mathematical programming, however, a considerable amount of symbolic transformation is essential to solving difficult optimization problems, e.g. relaxation or decomposition techniques. This step is usually carried out by hand, involves human ingenuity, and often constitutes the “theoretical contribution” of some research papers. We describe a ReformulationOptimization Software Engine (ROSE) for performing (automatic) symbolic computation on mathematical programming formulations.
Novel global optimization methods: . . .
, 2012
"... Allocating limited resources in process synthesis and operations is a major industrial challenge that is best approached using recent theoretical advances in global optimization. Relevant highthroughput applications include: petroleum refining; wastewater treatment; supplychain operations; oil wel ..."
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Allocating limited resources in process synthesis and operations is a major industrial challenge that is best approached using recent theoretical advances in global optimization. Relevant highthroughput applications include: petroleum refining; wastewater treatment; supplychain operations; oil well production. This dissertation begins by addressing the pooling problem, an optimization challenge of maximizing profit subject to product availability, storage capacity, demand, product specifications, and environmental standards. Pooling problems are particularly difficult instantiations of mixedinteger nonlinear programs (MINLP); this dissertation therefore expands to more broadly address two important classes of MINLP: mixedinteger quadratically constrained quadratic programs (MIQCQP) and mixedinteger signomial optimization problems (MISO). To solve both pooling problems and the more general classes, this dissertation incorporates three main strands: Effective modeling: This thesis formulates an extended pooling problem with the Environmental
Reduced RLT constraints for polynomial programming
"... Abstract. An extension of the reduced ReformulationLinearization Technique constraints from quadratic to general polynomial programming problems with linear equality constraints is presented and a strategy to improve the associated convex relaxation is proposed. 1. ..."
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Abstract. An extension of the reduced ReformulationLinearization Technique constraints from quadratic to general polynomial programming problems with linear equality constraints is presented and a strategy to improve the associated convex relaxation is proposed. 1.