Global optimization of bilinear programs with a multiparametric disaggregation technique

Kolodziej, Scott; Castro, Pedro; Grossmann, Ignacio E.

http://hdl.handle.net/10400.9/2445

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Authors

Kolodziej, Scott

Castro, Pedro

Grossmann, Ignacio E.

Abstract(s)

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scalemuchmore favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smallermixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.

Keywords

Mixed-integer linear programming Mixed-integer nonlinear programming Global optimization Quadratic optimization Disjunctive programming

URI

http://hdl.handle.net/10400.9/2445

Citation

Kolodziej, S.; Castro, P.M.; Grossmann, I.E. Global optimization of bilinear programs with a multiparametric disaggregation technique. In: Journal of Global Optimization, 2013, Vol. 57, nº 4, p. 1039-1063