Solving Mathematical Programs with Complementarity Constraints with Nonlinear Solvers
نویسنده
چکیده
S u m m a r y. MPCC can be solved with specific MPCC codes or in its nonlinear equivalent formulation (NLP) using NLP solvers. Two NLP solvers-NPSOL and the line search filter SQP-are used to solve a collection of test problems in AMPL. Both are based on SQP (Sequential Quadratic Programming) philosophy but the second one uses a line search filter scheme.
منابع مشابه
Interior-Point Algorithms, Penalty Methods and Equilibrium Problems
In this paper we consider the question of solving equilibrium problems—formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC’s)—as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get ar...
متن کاملA Hybrid Algorithm with Active Set Identification for Mathematical Programs with Complementarity Constraints∗
We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. To this end, we first introduce an active set identification technique. Then, by applying this technique to a smoothing continuation method presented ...
متن کاملNonlinear programming advances in mathematical programming with complementarity constraints
Given a suitably parameterised family of equilibrium models and a higher level criterion by which to measure an equilibrium state, mathematical programs with equilibrium constraints (MPECs) provide a framework for selecting good or even optimal parameters. An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll level...
متن کاملA Merit Function Piecewise SQP Algorithm for Solving Mathematical Programs with Equilibrium Constraints∗
In this paper we propose a merit function piecewise SQP algorithm for solving mathematical programs with equilibrium constraints (MPECs) formulated as mathematical programs with complementarity constraints. Under some mild conditions, the new algorithm is globally convergent to a piecewise stationary point. Moreover if the partial MPECLICQ is satisfied at the accumulation point then the accumul...
متن کاملOn Solving Mathematical Programs with Complementarity Constraints as Nonlinear Programs
We investigate the possibility of solving mathematical programs with complemen-tarity constraints (MPCCs) using classical algorithms and procedures from nonlinear programming. Although MPCCs do not satisfy a constraint qualiication, we establish suucient conditions for their Lagrange multiplier set to be nonempty in two diierent formulations. MPCCs that have nonempty Lagrange multiplier sets an...
متن کامل