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

In this paper, we extend the one-parametric class of merit functions proposed by Kanzow
and Kleinmichel [C. Kanzow, H. Kleinmichel, A new class of semismooth Newton-type …

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 …

We show that the gradient map** of the squared norm of Fischer–Burmeister function is
globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving …

It has been an open question whether the family of merit functions $\psi _p\(p> 1) $, the
generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is …

It is well-known that the scalar-valued FB function φ: R× R→ R is specified by φ (a, b):= a+
b−√ a2+ b2, a, b∈ R,(1.1) which is attributed by Fischer to Burmeister (see [5, 6, 7]). It is a …

For a locally optimal solution to the nonlinear semidefinite programming problem, under
Robinson's constraint qualification, we show that the nonsingularity of Clarke's Jacobian of …

This paper focuses on the study of differential properties of the symmetric matrix-valued
Fischer–Burmeister (FB) function. As the main results, the formulas for the directional …

In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz
continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this …

In this paper, the optimality conditions of semidefinite programming are transformed into an
unconstrained optimization problem based on a suitable merit function, which gradient is …