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Obtaining tighter relaxations of mathematical programs with complementarity constraints. (English) Zbl 1346.90686
Terlaky, Tamás (ed.) et al., Modeling and optimization: Theory and applications. Selected contributions from the MOPTA 2010 conference, Bethlehem, PA, USA, August 18–20, 2010. New York, NY: Springer (ISBN 978-1-4614-3923-3/hbk; 978-1-4614-3924-0/ebook). Springer Proceedings in Mathematics & Statistics 21, 1-23 (2012).
The authors consider linear programs with linear complementarity constraints, which belong to global optimization problems since their feasible set defined by complementarity conditions is non-convex and disjunctive. In order to find a solution of this non-convex optimization problem, one must use lower bounds of its optimal value by applying a suitable relaxation, where the initial problem is replaced by its convex approximation. The authors suggest several new ways for the approximation of linear complementarity conditions and the corresponding implementation algorithms. The computational results illustrate the usefulness of these techniques.
For the entire collection see [Zbl 1250.90012].

MSC:
90C26 Nonconvex programming, global optimization
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C59 Approximation methods and heuristics in mathematical programming
Software:
SDPLR; MacMPEC; CSDP; KNITRO
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