Youlin Shang

A new filled function method for unconstrained global optimization

In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191-204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.

A filled function method with one parameter for box constrained global optimization

In this paper, a new auxiliary function with one parameter on box constrained for escaping the current local minimizer of global optimization problem is proposed. First, a new definition of the filled function for box constrained minimization problem is given and under mild assumptions, this new auxiliary function is really a filled function. Then a new solution algorithm is proposed according to the theoretical analysis. And some numerical results demonstrate the efficiency of this method for box constrained global optimization.

Global minimization of non-smooth unconstrained problems with filled function

For smooth or non-smooth unconstrained global optimization problems, an one parameter filled function is derived to identify their global optimizers or approximately global optimizers. The theoretical properties of the proposed function are investigated. Based on the filled function, an algorithm is designed for solving unconstrained global optimization problems. The algorithm consists of two phases: local minimization and filling. The former is intended to minimize the objective function and obtain a local optimizer, the latter aims to find a better initial point for the first phase. Numerical experimentation is also provided. The preliminary computational results confirm that the proposed filled function approach is promising.

Modified T-F Function Method for Finding Global Minimizer on Unconstrained Optimization

This paper indicates that the filled function which appeared in one of the papers by Y. L. Shang et al. (2007) is also a tunneling function; that is, we prove that under some general assumptions this function has the characters of both tunneling function and filled function. A solution algorithm based on this T-F function is given and numerical tests from test functions show that our T-F function method is very effective in finding better minima.

An O(\sqrt{n}L) iteration Mehrotra-type predictor-corrector algorithm for monotone linear complementarity problem

In this paper we propose a new class of Mehrotra-type predictor-corrector algorithm for the monotone linear complementarity problems (LCPs). At each iteration, the method computes a corrector direction in addition to the Ai–Zhang direction (SIAM J Optim 16:400–417, 2005), in an attempt to improve performance. Starting with a feasible point

A new algorithm for constrained global optimization based on filled function

(x^0, s^0)

New Lagrangian Multiplier Method with NCP Function

(x0,s0) in the wide neighborhood