In this paper we present a penalty method for solving a complementarity problem involving 2nd-order nonlinear parabolic differential operators. In this work we first rewrite the complementarity problem as a nonlinear variational inequality. Then, we define a nonlinear parabolic partial differential equation (PDE) approximating the variational inequality using a power penalty term with a penalty...

In this paper, we present a new method of interior point to solve a class of the nonlinear problem of complementarity inspired from a study introduced by Censor et al. This method is regarded as reduction from the variational inequalities problem to a particular case. Under less restrictive constraints, we are able to generate a sequence of nonnegative elements and we establish the global conve...

Analogous to the nonlinear complementarity problem (NCP) and the semidefinite complementarity problem (SDCP), a popular approach to solving the secondorder cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over IR. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP ...

We investigate the properties of a new merit function which allows us to reduce a nonlinear complementarity problem to an unconstrained global minimization one. Assuming that the complementarity problem is deened by a P 0-function we prove that every stationary point of the unconstrained problem is a global solution; furthermore, if the complementarity problem is deened by a uniform P-function,...

In this paper, we consider the tensor eigenvalue complementarity problem which is closely related to the optimality conditions for polynomial optimization, as well as a class of differential inclusions with nonconvex processes. By introducing an NCP-function, we reformulate the tensor eigenvalue complementarity problem as a system of nonlinear equations. We show that this function is strongly s...