This paper extends the Lagrangian globalization (LG) method to the nonsmooth equation Φ(x) = 0 arising from nonlinear complementarity problems NCP and presents a descent algorithm for the LG phase. The aim of this paper is not to present a new method for solving NCP, but to find x̂ such that ‖Φ(x̂)‖ < ‖Φ(x̄)‖ when the NCP has a solution and x̄ is a stationary point but not a solution.

In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric user equilibria. By applying various reformulation...

The paper discusses three general classes of nonlinear programming models. Our objective is to show how to represent optimization problem, such as nonlinear programs, in a compact format using extended mathematical programming. This is a useful tool, especially in cases when complementarity representation, such as mixed complementarity problems, could be difficult to apply. We reflect on the sp...

Here we present a primal-dual interior point nonmonotone line search filter method for nonlinear programming. The filter relies on three measures, the feasibility, the complementarity and the optimality presented in the optimality conditions, considers relaxed acceptability criteria for the step size and includes a feasibility restoration phase. The evaluation of the method is until now made on...

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...