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QPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints
"... . 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, firstlevel constraints are linear, and secondlevel (equilibrium) co ..."
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. 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, firstlevel constraints are linear, and secondlevel (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, illconditioning, convexity of the objective, monotonicity and symmetry of the secondlevel 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.maths.mu.OZ.AU/~danny/qpecgendoc.h...
A TrustRegion Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience
, 2005
"... We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upperlevel objective and all constraintdefining functions, as well as a quadratic approximation of the lowerlevel objective ..."
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Cited by 4 (0 self)
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We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upperlevel objective and all constraintdefining functions, as well as a quadratic approximation of the lowerlevel objective. We describe the main features of the algorithm and the resulting software. Numerical experiments tend to confirm the promising behavior of the method.
Generating Quadratic Bilevel Programming Test Problems
 CODEN ACMSCU. ISSN 00983500. URL http://www. acm.org/pubs/citations/journals/ toms/1994201/p103calamai/; http: //doi.acm.org/10.1145/174603.174411
, 1994
"... This paper describes a technique for generating sparse or dense quadratic bilevel programming problems with a selectable number of known global and local solutions. The technique described here does not require the solution of any subproblems. In addition, since most techniques for solving these pro ..."
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Cited by 2 (0 self)
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This paper describes a technique for generating sparse or dense quadratic bilevel programming problems with a selectable number of known global and local solutions. The technique described here does not require the solution of any subproblems. In addition, since most techniques for solving these problems begin by solving the corresponding relaxed quadratic program, the global solutions are constructed to be different than the global solution of this relaxed problem in a selectable number of upper and lowerlevel variables. Finally, the problems that are generated satisfy the requirements imposed by all the solution techniques known to the authors. Categories and Subject Descriptors: G.4 [Mathematics of Computing]: