We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax − |x| = b, where A is an arbitrary n × n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give no...

A Mathematical Program with Linear Complementarity Constraints (MPLCC) is an optimization problem where a continuously differentiable function is minimized on a set defined by linear constraints and complementarity conditions on pairs of complementary variables. This problem finds many applications in several areas of science, engineering and economics and is also an important tool for the solu...

For any system of linear inequalities, consistent or not, the norm of the violations of the inequalities by a given point, multiplied by a condition constant that is independent of the point, bounds the distance between the point and the nonempty set of points that minimize these violations. Similarly, for a dual pair of possibly infeasible linear programs, the norm of violations of primal-dual...

The paper offers a universal method for finding a unique or multiple DC operating points of nonlinear circuits. The developed method is based on the theory known as a linear complementarity problem (LCP) and the homotopy concept. It is a combination of Lemke’s method for solving LCP and some variant of the homotopy method. To express the problem of finding DC operating points in terms of LCP, a...

This paper presents some fundamental results about sufficient linear weighted complementarity problems. Such a problem depends on a nonnegative weight vector. If the weight vector is zero, the problem reduces to a sufficient linear complementarity problem that has been extensively studied. The introduction of the more general notion of a weighted complementarity problem (wCP) was motivated the ...

A unified formulation as well as numerical approach is presented both for the twoand three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a Second-Order Cone Linear Complementarity Problem (SOCLCP) is formulated, which consists of complementarity conditions defined by the bilinear functions and the se...

A unified formulation and a numerical approach are presented for twoand three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a Second-Order Cone Linear Complementarity Problem (SOCLCP) is formulated, which consists of complementarity conditions defined by bilinear functions and second-order cone const...

A new formulation is presented for the three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a second-order cone linear complementarity problem is formulated, which consists of complementarity conditions defined by bilinear functions and second-order cone constraints. The equilibrium configurations are...

Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proo...

A new method namely, algebraic elimination method is proposed for finding a complementarity feasible solution to the linear complementarity problem which have applications in non-linear programming, economics, game theory and engineering. Then, the algebraic elimination method is extended to quadratic programming problems. The solution procedure is illustrated by means of numerical examples.