A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems

A truncated aggregate smoothing Newton method for minimax problems

Aggregate function is a useful smoothing function to the max-function of some smooth functions and has been used to solve minimax problems, linear and nonlinear programming, generalized complementarity problems, etc. The aggregate function is a single smooth but complicated function, its gradient and Hessian calculations are timeconsuming. In order to gain more efficient performance of aggregat...

A Smoothing Newton Method for Semi-Infinite Programming

A Regularized Smoothing Newton Method for Symmetric Cone Complementarity Problems

This paper extends the regularized smoothing Newton method in vector optimization to symmetric cone optimization, which provide a unified framework for dealing with the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem (SCCP). In particular, we study strong semismoothness and Jacobian nonsingularity of the total natura...

Smoothing Functions and A Smoothing Newton Method for Complementarity and Variational Inequality Problems

In this paper, we discuss smoothing approximations of nonsmooth functions arising from complementarity and variational inequality problems. We present some new results which are essential in designing Newton-type methods. We introduce several new classes of smoothing functions for nonlinear complementarity problems and order complementarity problems. In particular, in the first time some comput...

Solving semi-infinite programs by smoothing projected gradient method

In this paper, we study a semi-infinite programming (SIP) problem with a convex set constraint. Using the value function of the lower level problem, we reformulate SIP problem as a nonsmooth optimization problem. Using the theory of nonsmooth Lagrange multiplier rules and Danskin’s theorem, we present constraint qualifications and necessary optimality conditions. We propose a new numerical meth...