The nonlinear complementarity problem is cast as an unconstrained minimization problem that is obtained from an augmented Lagrangian formulation. The dimensionality of the unconstrained problem is the same as that of the original problem, and the penalty parameter need only be greater than one. Another feature of the unconstrained problem is that it has global minima of zero at precisely all th...

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 we construct a regularization Newton method for solving the nonlinear complementarity problem (NCP(F)) and analyze its convergence properties under the assumption that F is a P0-function. We prove that every accumulation point of the sequence of iterates is a solution of NCP(F) and that the sequence of iterates is bounded if the solution set of NCP(F) is nonempty and bounded. More...

In this paper, by using the smoothing Fischer-Burmeister function, we present a new smoothing conjugate gradient method for solving the nonlinear nonsmooth complementarity problems. The line search which we used guarantees the descent of the method. Under suitable conditions, the new smoothing conjugate gradient method is proved globally convergent. Finally, preliminary numerical experiments sh...

̈ find x ∈ R s. t. x i ≥ 0, Fi(x)≥ 0, x iFi(x) = 0, for i = 1, · · · ,n, where F(x) : R → R is assumed to be continuously differentiable. There have been extensive studies for complementarity problems, see for example [5] and a recent review paper [7]. The NCP was introduced by Cottle [4] in his Ph.D. thesis in 1964. At the beginning, it was recognized that the NCP is a special case of a variati...

We generalize the P, P0, R0 properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of generalized nonlinear complementarity problem (GNCP). We prove that if a continuous function has the order P0 and R0 properties then all the associated GNCPs have solutions.

NE/SQP is a recent algorithm tha t has proven quite effective for solving the pure and mixed forms of the nonlinear complementarity problem (NCP). NE/SQP is robust in the sense that i ts direction-finding subproblems are always solvable; in addition, the convergence rate of this method is Q-quadratic. In this paper we consider a generalized version of NE/SQP proposed by Pang and Qi, that is sui...