Comments on: Algorithms for linear programming with linear complementarity constraints 2
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S. Dempe [1]
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[1] TU Bergakademie Freiberg, Alemania
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- Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 20, Nº. 1, 2012, págs. 28-29
- Idioma: inglés
- Enlaces
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Resumen
In the paper nonconvex optimization problems are considered which can be transformed into mathematical programming problems with linear complementarity constraints (abbreviated as (GLPC)). For those problems algorithms are presented for calculating feasible, stationary resp. global optimal solutions. The investigation of nonconvex optimization problems is a very challenging topic. Algorithms solving them often compute stationary points (e.g. F.-John- or Karush–Kuhn–Tucker points). But from an the view of applications sometimes the computation of a global optimal solution is necessary. Then, algorithms need to be applied which often combine approaches in combinatorial optimization (as e.g. branch-and-bound) with convex approximations of the problem (see e.g. Horst and Tuy 1990; Meyer and Floudas 2005). Another approach is to transform those problems into well investigated equivalent problems. This is the way suggested in the paper by J.J. Judice for different problems: bilevel programming with convex quadratic lower level problems; bilinear problems; nonconvex quadratic and absolute value problems. For the bilevel programming problems equivalence between both problems can be guaranteed only if global optimal solutions are computed, see Dempe and Dutta (to appear).
