1,560 research outputs found
Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework
We present a new framework for the solution of mathematical programs with
equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is
viewed as a concentration of an unconstrained optimization which minimizes the
complementarity measure and a nonlinear programming with general constraints. A
strategy generalizing ideas of Byrd-Omojokun's trust region method is used to
compute steps. By penalizing the tangential constraints into the objective
function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like
strategy is used to balance the improvements on feasibility and optimality. We
show that, under MPEC-MFCQ, if the algorithm does not terminate in finite
steps, then at least one accumulation point of the iterates sequence is an
S-stationary point
Optimal control of Allen-Cahn systems
Optimization problems governed by Allen-Cahn systems including elastic
effects are formulated and first-order necessary optimality conditions are
presented. Smooth as well as obstacle potentials are considered, where the
latter leads to an MPEC. Numerically, for smooth potential the problem is
solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an
obstacle potential first numerical results are presented
AN INTERIOR-POINT METHOD FOR MPECs BASED ON STRICTLY FEASIBLE RELAXATIONS.
An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation scheme preserves the nonempty strict feasibility of each subproblem even in the limit. Local and superlinear convergence of the algorithm is proved even with a less restrictive strict complementarity condition than the standard one. Moreover, mechanisms for inducing global convergence in practice are proposed. Numerical results on the MacMPEC test problem set demonstrate the fast-local convergence properties of the algorithm.
An interior-point method for mpecs based on strictly feasible relaxations.
An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation scheme preserves the nonempty strict feasibility of each subproblem even in the limit. Local and superlinear convergence of the algorithm is proved even with a less restrictive strict complementarity condition than the standard one. Moreover, mechanisms for inducing global convergence in practice are proposed. Numerical results on the MacMPEC test problem set demonstrate the fast-local convergence properties of the algorithm
Solving a signalized traffic intersection problem with NLP solvers
Mathematical Programs with Complementarity Constraints (MPCC) finds many applications in areas such engineering design, economic equilibrium and mathematical theory itself. In this work we consider a queuing system model resulting from a single signalized traffic intersection regulated by
pre-timed control in an urban traffic network. The model is formulated as an MPCC problem and
may be used to ascertain the optimal cycle and the green split allocation. This MPCC problem is
also formulated as its NLP equivalent reformulation. The goal of this work is to solve the problem,
using both MPCC and NLP formulations, minimizing two objective functions: the average queue
length over all queues and the average waiting time over the worst queue. The problem was codified
in AMPL and solved using some optimization software packages.Fundação para a Ciência e a Tecnologia (FCT) FCOMP-01-0124-FEDER-022674 (R&D unit Algoritmi)PEst-OE/MAT/UI4080/201
Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints
On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested
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