In this paper, the authors describe and establish the convergence of a new iterative method for solving the (nonmonotone) nonlinear complementarity problem (NCP). The method utilizes ideas from two distinct approaches for solving this problem and combines them into one unified framework. One of these is the infeasible-interior-point approach that computes an approximate solution to the NCP by s...

We propose two line search primal-dual interior-point methods that approximately solve a sequence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an `2-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter rema...

All forms of the simplex method reach the optimum by traversing a series of basic solutions. Since each basic solution represents an extreme point of the feasible region, the track followed by the algorithm moves around the boundary of the feasible region. In the worst case, it may be necessary to examine most if not all of the extreme points. This can be cripplingly inefficient given that the ...

In this paper we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problem (HLCP). This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by suitable perturbation in HLCP problem. Then, we use so-called feasibility steps that serves to generate strictly feasible iterates for the ...

In this paper, we propose a Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for symmetric optimization using the arc-search strategy. The proposed algorithm searches for optimizers along the ellipses that approximate the central path and ensures that the duality gap and the infeasibility have the same rate of decline. By analyzing, we obtain the iteration complexity [Formula...

It has been noticed by Wächter and Biegler that a number of interior point methods for nonlinear programming based on line search strategy may generate a sequence converging to an infeasible point. We show that by adopting a suitable merit function, a modified primal-dual equation, and a proper line search procedure, a class of interior point methods of line search type will generate a sequence...

Re-optimization techniques for an interior point method applied to solve a sequence of linear programming problems are discussed. Conditions are given for problem perturbations that can be absorbed in merely one Newton step. The analysis is performed for both short-step and long-step feasible path-following method. A practical procedure is then derived for an infeasible path-following method. I...

This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classical decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a primal-dual infeasible interior point method. The above-mentioned algorithm ooers a perfect measure of...

This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classical decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a primal-dual infeasible interior point method. The abovementioned algorithm o ers perfect measure of th...