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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 Bilevel Approach for Traffic Management in Capacitated Networks
, 2008
"... We consider a bilevel programming (or leader’s) problem with linear lowerlevel (or follower’s) problem. Under a regularity condition based on the stability regions for the follower’s problem, some simple optimality conditions are derived for the leader’s problem. Furthermore, we apply this model to ..."
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We consider a bilevel programming (or leader’s) problem with linear lowerlevel (or follower’s) problem. Under a regularity condition based on the stability regions for the follower’s problem, some simple optimality conditions are derived for the leader’s problem. Furthermore, we apply this model to the formulation of a traffic control problem designed to solve problems including accidents and/or pollution alleviation on some parts of a road networks.