Fuzzy-Enforced Complementarity Constraints in Nonlinear Interior Point Method-Based Optimization

Interior-point Methods for Nonconvex Nonlinear Programming: Complementarity Constraints

In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interior-point method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerica...

A New Interior Point Method for Nonlinear Complementarity Problem

In this paper, we present a new method of interior point to solve a class of the nonlinear problem of complementarity inspired from a study introduced by Censor et al. This method is regarded as reduction from the variational inequalities problem to a particular case. Under less restrictive constraints, we are able to generate a sequence of nonnegative elements and we establish the global conve...

Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems

Extending our previous work Monteiro and Pang (1996), this paper studies properties of two fundamental mappings associated with the family of interior-point methods for solving monotone nonlinear complementarity problems over the cone of symmetric positive semideenite matrices. The rst of these maps lead to a family of new continuous trajectories which include the central trajectory as a specia...

A New Interior Point Algorithm for Nonlinear Complementarity Problems

1. Abstract The complementarity problem consists in finding x ∈ IR such that x ≥ 0 , F (x) ≥ 0 and xF (x) = 0, where F : IR → IR. Complementarity problems are involved in several applications in engineering, economy and different branches of physics . We mention contact problems and dynamics of multiple bodies systems in solid mechanics. In this paper we present a new feasible interior point al...