A popular approach to solving the nonlinear complementarity problem (NCP) is to reformulate it as the global minimization of a certain merit function over ℝn.Expand

We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiable, continuous differentiability and (ρ-order) semismoothness.Expand

We propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+∞), and show several favorable properties of the proposed functions.Expand

We consider two classes of proximal-like algorithms for minimizing a proper lower semicontinuous quasi-convex function f(x) subject to non-negative constraints $$x \geq 0$.Expand

We symmetrize the generalized natural residual NCP-function, a natural extension of the Fischer-Burmeister function that does not possess symmetric graph, and construct not only new N CP-functions and merit functions for the nonlinear complementarity problem, but also provide parallel functions to the generalized Fischer-burmeister functions.Expand

We investigate a one-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) which is closely related to the popular Fischer–Burmeister (FB) merit function and natural residual merit function.Expand

We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the Semismooth Newton's method.Expand

We propose a class of interior proximal-like algorithms for the second- order cone program, which is to minimize a closed proper convex function subject to general second-order cone constraints.Expand