A hierarchy of relaxations for nonlinear convex generalized disjunctive programming

Juan P. Ruiz and Ignacio E. Grossmann

European Journal of Operational Research, 2012, vol. 218, issue 1, 38-47

Abstract: We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of the relaxations increases as the number of conjuncts decreases, leading to a hierarchy of relaxations. We prove that the tightest of these relaxations, allows in theory the solution of the disjunctive convex program as a nonlinear programming problem. We present a methodology to guide the generation of strong relaxations without incurring an exponential increase of the size of the reformulated mixed-integer program. Finally, we apply the theory developed to improve the computational efficiency of solution methods for nonlinear convex generalized disjunctive programs (GDP). This methodology is validated through a set of numerical examples.

Keywords: Combinatorial optimization; Convex programming; Disjunctive programming; Generalized disjunctive programming; Tight relaxations (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:218:y:2012:i:1:p:38-47

DOI: 10.1016/j.ejor.2011.10.002

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