In this paper, a trust region method for generalized semi-infinite programming problems is presented. The method is based on [O. Yi-gui, “A filter trust region method for solving semi-infinite programming problems”, J. Appl. Math. Comput. 29, 311 (2009)]. We transformed the method from standard to generalized semi-infinite programming problems. The semismooth reformulation of the Karush–Kuhn–Tu...

Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Most state-of-the-art techniques treat the discontinuous dynamics of contact as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning through contact that eliminates the r...

We introduce a new NCP-function that reformulates a nonlinear com-plementarity problem as a system of semismooth equations (x) = 0. The new NCP-function possesses all the nice properties of the Fischer-Burmeister function for local convergence. In addition, its natural merit function (x) = 1 2 (x) T (x) has all the nice features of the Kanzow-Yamashita-Fukushima merit function for global conver...

We prove a new local convergence property of some primal-dual methods for solving nonlinear optimization problems. We consider a standard interior point approach, for which the complementarity conditions of the original primal-dual system are perturbed by a parameter driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed system and by app...

In this paper, the authors describe and establish the convergence of a new iterative method for solving the (nonmonotone) nonlinear complementarity problem (NCP). The method utilizes ideas from two distinct approaches for solving this problem and combines them into one unified framework. One of these is the infeasible-interior-point approach that computes an approximate solution to the NCP by s...

In this paper we propose a class of new large-update primal-dual interior-point algorithms for P∗(κ) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.’s for P∗(κ) complementarity problem based on the self-regular functio...

A power penalty approach has been proposed to linear complementarity problem but not to Horizontal Linear Complementarity Problem (HLCP) because the coefficient matrix is not positive definite. It is skillfully proved that HLCP is equivalent to a variational inequality problem and a mixed linear complementarity problem for the first time. A power penalty approach is proposed to the mixed linear...

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...