Abstract
A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.
Highlights
Because of advances in science, economics and engineering, studies on global optimization for multi-minimum nonlinear programming problem P : minx∈Rn f x have become a topic of great concern
The idea behind the filled function methods is to construct an auxiliary function that allows us to escape from a given local minimum of the original objective function
We first give a definition of a filled function for a non-smooth unconstrained minimization problem and construct a new filled function with two parameters
Summary
Because of advances in science, economics and engineering, studies on global optimization for multi-minimum nonlinear programming problem P : minx∈Rn f x have become a topic of great concern. Most existing methods deal only with the first issue Among these methods, the filled function method is a practical useful tool for global optimization. The idea behind the filled function methods is to construct an auxiliary function that allows us to escape from a given local minimum of the original objective function It consists of two phase: local minimization and filling. We modify the concept of filled function presented by 10 and propose a novel class of filled function for non-smooth the global optimization.
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