395 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
Solving mathematical programs with complementarity constraints with nonlinear solvers
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.(undefined
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
A smoothing SQP method for nonlinear programs with stability constraints arising from power systems
This paper investigates a new class of optimization problems arising from power systems, known as nonlinear programs with stability constraints (NPSC), which is an extension of ordinary nonlinear programs. Since the stability constraint is described generally by eigenvalues or norm of Jacobian matrices of systems, this results in the semismooth property of NPSC problems. The optimal conditions of both NPSC and its smoothing problem are studied. A smoothing SQP algorithm is proposed for solving such optimization problem. The global convergence of algorithm is established. A numerical example from optimal power flow (OPF) is done. The computational results show efficiency of the new model and algorithm. © The Author(s) 2010.published_or_final_versionSpringer Open Choice, 21 Feb 201
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.
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
Combining the regularization strategy and the SQP to solve MPCC - A MATLAB implementation
Mathematical Program with Complementarity Constraints (MPCC) plays a very
important role in many fields such as engineering design, economic equilibrium,
multilevel game, and mathematical programming theory itself. In theory its constraints
fail to satisfy a standard constraint qualification such as the linear independence
constraint qualification (LICQ) or the Mangasarian-Fromovitz constraint
qualification (MFCQ) at any feasible point. As a result, the developed nonlinear
programming theory may not be applied to MPCC class directly. Nowadays, a natural
and popular approach is try to find some suitable approximations of an MPCC
so that it can be solved by solving a sequence of nonlinear programs.
This work aims to solve the MPCC using nonlinear programming techniques,
namely the SQP and the regularization scheme. Some algorithms with two iterative
processes, the inner and the external, were developed. A set of AMPL problems
from MacMPEC database [7] were tested. The algorithms performance comparative
analysis was carried out
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