Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Andreas Löhne () and Andrea Wagner ()
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Andreas Löhne: Friedrich Schiller University Jena
Andrea Wagner: Vienna University of Economics and Business

Journal of Global Optimization, 2017, vol. 69, issue 2, No 4, 369-385

Abstract: Abstract A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $$f=g-h$$ f = g - h of two convex functions g and h. In particular, we deal with the special case where one of the two convex functions g or h is polyhedral. In case g is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case h is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex programs. Since polyhedral projection is equivalent to multiple objective linear programming (MOLP), a MOLP solver (in the second case together with a convex programming solver) can be used to solve instances of DC programs with polyhedral component. Numerical examples are provided, among them an application to locational analysis.

Keywords: DC programming; Global optimization; Polyhedral projection; Multiple objective linear programming; Linear vector optimization; 15A39; 52B55; 90C29; 90C05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-017-0519-8

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