Affine variational inequalities (AVI) are an important problem class that generalize systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. This paper describes PATHAVI, a structure-preserving pivotal approach, that can process (solve or determine infeasible) large-scale sparse instances of the problem efficiently, with theoretical guarant...

A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also...

This chapter presents continuous paths leading to the set of optimal solutions of a linear programming problem. These paths are derived from the weighted logarithmic barrier function. The defining equations are bilinear and have some nice primal-dual symmetry properties. Extensions to the general linear complementarity problem are indicated.

This paper proposes a globally convergent predictor-corrector infeasible-interiorpoint algorithm for the monotone semide nite linear complementarity problem using the AlizadehHaeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.

In this paper, we propose primal-dual potential-reduction algorithms which can start from an infeasible interior point. We rst describe two such algorithms and show that both are polynomial-time bounded. One of the algorithms decreases the Tanabe-Todd-Ye primal-dual potential function by a constant at each iteration under the condition that the duality gap decreases by at most the same ratio as...

The equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalization of Nash equilibrium problem (NEP) and the mathematical program with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a special class of EPECs where a common parametric P-matrix linear compl...

In this paper, we aim to solve an inverse robust optimization problem, in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this inverse problem as a minimization problem with a linear equality constraint, a second-order cone complementarity constrain...

We deene a minimization problem with simple bounds associated to the horizontal linear complementarity problem (HLCP). When the HLCP is solvable, its solutions are the global minimizers of the associated problem. When the HLCP is feasible, we are able to prove a number of properties of the stationary points of the associated problem. In many cases, the stationary points are solutions of the HLC...

Specially structured linear complementarity problems (LCPs) and their solution by the miss-cross method are examined. The criss-cross method is known to be finite for LCPs with positive semidefinite bisymmetric matrices and with P-matrices. It is also a simple finite algorithm for oriented matroid programming problems. Recently Cottle, Pang, and Venkateswaran identified the class of (column, ro...

In this paper, a monotone linear complementarity reformulation of the nonnegative least squares problems in inequality sense is introduced. Then Mehrotra’s predictor-corrector interior point algorithm is applied to solve the resulting monotone linear complementarity problem. Our numerical experiments on several randomly generated test problems show that Mehrotra’s algorithm overperforms the wid...