Combining nonmonotone trust region algorithms and PSO methods, we propose a mixed method for nonlinear complementarity problems. The iterative formula of k μ is very simple. When the determinant of k k B I λ + is very large or small, the PSO method will obtain a new point which gets us better astringency. Numerical test results show the effectiveness of this algorithm.

or to conclude that no such vectors ω, z exist. The inequalities appearing in (1) and in the sequel are understood componentwise and o denotes the zero vector. Many applications and solution methods for (1) can be found in [3] and [4], respectively. In [8] (see also Section 9.2 in [4]), the so-called modulus algorithm was developed for solving the LCP: Let I denote the identity and with x ∈ R w...

We consider the stochastic nonlinear complementarity problem (SNCP). We first formulate the problem as a stochastic mathematical program with equilibrium constraints and then, in order to develop efficient algorithms, we give some reformulations of the problem. Furthermore, based on the reformulations, we propose a smoothed penalty method for solving SNCP. A rigorous convergence analysis is als...

A family of Least-Change Secant-Update methods for solving nonlinear complementarity problems based on nonsmooth systems of equations is introduced. Local and superlinear convergence results for the algorithms are proved. Two different reformulations of the nonlinear complementarity problem as a nonsmooth system are compared, both from the theoretical and the practical point of view. A global a...

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obta...

We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCP-function-based reformulations of infinite-dimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our results generalize semismoothness and -order semismoothness from finite-dimensional spaces to a Banach...

In this paper, we introduce a new P -type condition for nonlinear functions defined over Euclidean Jordan algebras, and study a continuation method for nonlinear complementarity problems over symmetric cones. This new P -type condition represents a new class of nonmonotone nonlinear complementarity problems that can be solved numerically.

In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonst...

We present a method for smoothing discontinuous dynamics involving contact and friction, thereby facilitating the use of local optimization techniques for control. The method replaces the standard Linear Complementarity Problem with a Stochastic Linear Complementarity Problem. The resulting dynamics are continuously differentiable, and the resulting controllers are robust to disturbances. We de...