Convergence Analysis of an Interior-point Method for Mathematical Programs with Equilibrium Constraints
نویسندگان
چکیده
We prove local and global convergence results for an interior-point methodapplied to mathematical programs with equilibrium constraints. The globalresult shows the algorithm minimizes infeasibility regardless of startingpoint, while one result proves local convergence when penalty functions areexact; another local result proves convergence when the solution is not evena KKT point.
منابع مشابه
Convergence Analysis of an Interior-point Method for Nonconvex Nonlinear Programming
In this paper, we present global and local convergence results for an interior-point method for nonlinear programming. The algorithm uses an `1 penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’s strictly feasible interior-point method [6]. The global conver...
متن کاملA two-sided relaxation scheme for Mathematical Programs with Equilibrium Constraints
We propose a relaxation scheme for mathematical programs with equilibrium constraints (MPECs). In contrast to previous approaches, our relaxation is two-sided: both the complementarity and the nonnegativity constraints are relaxed. The proposed relaxation update rule guarantees (under certain conditions) that the sequence of relaxed subproblems will maintain a strictly feasible interior—even in...
متن کاملGlobal convergence of an inexact interior-point method for convex quadratic symmetric cone programming
In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programmin...
متن کاملInterior-point Methods for Nonconvex Nonlinear Programming: Convergence Analysis and Computational Performance
In this paper, we present global and local convergence results for an interior-point method for nonlinear programming and analyze the computational performance of its implementation. The algorithm uses an `1 penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’...
متن کاملGeneralized stationary points and an interior-point method for mathematical programs with equilibrium constraints
Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or the...
متن کامل