In this paper, we propose a projection method for solving a system of nonlinear monotone equations with convex constraints. Under standard assumptions, we show the global convergence and the linear convergence rate of the proposed algorithm. Preliminary numerical experiments show that this...

The Order-Value Optimization (OVO) problem is a generalization of the classical Minimax problem. Instead of the maximum of a set functions, the functional value that ranks in the p-th place is minimized. The problem seeks the application to (non-pessimistic) decision making and to model fitting...

The solution of an equation f(x)=γ given by an increasing function f on an interval I and right-hand side γ, can be approximated by a sequence calculated according to Newton’s method. In this article, global convergence of the method is considered in the strong sense of convergence for any...

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer’s approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method. Our...

In this paper, a new trust region method is presented for general constrained optimization problem. In this algorithm, the trial step is obtained by solving two quadratic programming problems with bound constraints. The algorithm is implementable easily. Then we prove that the method is globally...

In this paper, for solving variational inequality problems (VIPs) we propose a feasible descent algorithm via minimizing the regularized gap function of Fukushima. Under the condition that the underlying mapping of VIP is strongly monotone, the algorithm is globally convergent for any...

An active set limited memory BFGS algorithm for large-scale bound constrained optimization is proposed. The active sets are estimated by an identification technique. The search direction is determined by a lower dimensional system of linear equations in free subspace. The implementations of the...

In this paper, an extended form of the entropic perturbation method of linear programming is given, which can overcome the weakness of the original method – being easy of overflow in computing. Moreover, the global convergence of the gradient algorithm for the method is discussed. Copyright...

In this paper we propose a non-interior-point smoothing algorithm for solving the monotone nonlinear complementarity problem (NCP). The proposed algorithm is simpler than many existing non-interior-point smoothing algorithms in the sense that it only needs to solve one system of linear equations...

A new smoothing approach was given for solving the mathematical programs with complementarity constraints (MPCC) by using the aggregation technique. As the smoothing parameter tends to zero, if the KKT point sequence generated from the smoothed problems satisfies the second-order necessary...