mpcc – Page 2 – Optimization Online

Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints

Published: 2002/09/02

Complementarity and Variational Inequalities, Constrained Nonlinear Optimization complementarity constraints, complementarity problem, mathematical programs with equilibrium constraints, mpcc, mpec, piecewise sequential quadratic programming, quasi-newton methods, superlinear convergence

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

Convergence of a Penalty Method for Mathematical Programmingwith ComplementarityConstraints

Published: 2002/09/02, Updated: 2002/09/09

Xinmin Hu

Daniel Ralph

Complementarity and Variational Inequalities, Constrained Nonlinear Optimization b-stationarity, complementarity constraints, linear independence constraint qualification, mpcc, mpec, penalty methods

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

A stable homotopy approach to horizontal linear complementarity problems

Published: 2002/09/02

Daniel Ralph

Complementarity and Variational Inequalities active set method, global metric regularity, homotopy method, horizontal linear complementarity problem, mathematical program with complementarity constraints, mpcc, mpcc-licq, mpec, path following, piecewise affine system, pseudo-lipschitz continuity, qpcc, stable solution

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

Local convergence of SQP methods for Mathematical Programs with Equilibrium Constraints

Published: 2002/05/09, Updated: 2002/05/29

Complementarity and Variational Inequalities, Constrained Nonlinear Optimization equilibrium constraints, mpcc, mpec, nonlinear programming, sequential quadratic programming

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

The Penalty Interior Point Method fails to converge for Mathematical Programs with Equilibrium Constraints

Published: 2002/05/09

Sven Leyffer

Complementarity and Variational Inequalities, Constrained Nonlinear Optimization equilibrium constraints, interior point methods, mpcc, mpec, nonlinear programming, pipa

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. CitationNumerical Analysis Report NA/208, Department of Mathematics, University of Dundee, February 2002.ArticleDownload View PDF