We present a new formulation of the truss topology problem that results in unique design and unique displacements of the optimal truss. This is reached by adding an upper level to the original optimization problem and formulating the new problem as an MPCC (Mathematical Program with Complementarity Constraints). We derive optimality conditions for this problem … Read more
We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to “right-hand-side perturbations” of the data, hence are numerically attractive. The main purpose of the paper is to show how the … Read more
Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are … Read more
We adapt the convergence analysis of smoothing (Fukushima and Pang) and regularization (Scholtes) methods to a penalty framework for mathematical programs with complementarity constraints (MPCCs), and show that the penalty framework shares similar convergence properties to these methods. Moreover, we give sufficient conditions for a sequence generated by the penalty framework to be attracted to … Read more
This paper describes numerical experience with solving MPECs as NLPs on a large collection of test problems. The key idea is to use off-the-shelf NLP solvers to tackle large instances of MPECs. It is shown that SQP methods are very well suited to solving MPECs and at present outperform Interior Point solvers both in terms … Read more
This paper presents a small example for which the Penalty Interior Point Method converges to a non-stationary point. The reasons for this adverse behaviour are discussed. Citation Numerical Analysis Report NA/208, Department of Mathematics, University of Dundee, February 2002. Article Download View The Penalty Interior Point Method fails to converge for Mathematical Programs with Equilibrium … Read more
Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs). In particular, Sequential Quadratic Programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. It is shown that SQP converges superlinearly under reasonable assumptions … Read more