QPECgen, a MATLAB Generator for Mathematical Programs with Quadratic Objectives and Affine Variational Inequality Constraints |
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Authors: | Houyuan Jiang Daniel Ralph |
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Affiliation: | (1) Department of Mathematics and Statistics, The University of Melbourne, Parkville, Vic, 3052, Australia |
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Abstract: | We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html. |
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Keywords: | mathematical programs with equilibrium constraints bilevel program constrained optimization quadratic program with affine variational inequality constraints degeneracy ill-conditioning optimality conditions variational inequality complementarity problem MATLAB test problem generator |
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