In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, ...

In this paper, we first give a new equivalent optimization form to nonlinear complementarity problems and then establish a damped Newton method in which penalty technique is used. The subproblems of the method are lower-dimensional linear complementarity problems. We prove that the algorithm converges globally for strongly monotone complementarity problems. Under certain conditions, the method ...

In this paper we first present a mathematical programming problem, the Extended Linear Complementarity Problem (ELCP). Next we discuss how the ELCP can be used to solve some basic problems in the system theory for a class of discrete event systems that can be modeled using the max-plus algebra, which has maximization and addition as basic operations. Finally we show that the ELCP also appears i...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...

The linear complementarity problem (LCP) is one of the most widely studied mathematical programming problems. The theory of LCP can be extended to oriented matroids which are combinatorial abstractions of linear subspaces of Euclidean spaces. This paper briefly surveys the LCP, oriented matroids and algorithms for the LCP on oriented matroids. key words: linear complementarity problem, oriented...

We present an infeasible-interior-point algorithm for monotone linear complementarity problems in which the search directions are affine scaling directions and the step lengths are obtained from simple formulae that ensure both global and superlinear convergence. By choosing the value of a parameter in appropriate ways, polynomial complexity and convergence with Q-order up to (but not including...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...