On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory

Richard Oberdieck, Nikolaos A. Diangelakis, Styliani Avraamidou and Efstratios N. Pistikopoulos ()
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Richard Oberdieck: Imperial College London
Nikolaos A. Diangelakis: Imperial College London
Styliani Avraamidou: Imperial College London
Efstratios N. Pistikopoulos: Texas A&M University

Journal of Global Optimization, 2017, vol. 69, issue 3, No 4, 587-606

Abstract: Abstract In multi-parametric programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-parametric quadratic programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the parametric solution of the dual of a convex problem.

Keywords: Unbounded problems; Binary parameters; Multi-parametric programming; Mixed-integer bilevel programming (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-016-0463-z

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