APPLICATION OF HARMONIC FUNCTION’S THEORY IN TWO-DIMENSION OPTIMIZATION PROBLEM

Abstract

The mathematical models of many engineering problems can often come down to two-dimensional optimization problems,it has been one of the hot issues of seeking the high effective and precision optimizing method.The characteristics of harmonic function and Green theory were used to study the relations between the values of harmonic function and its boundary values,and demonstrate the non-locality of its extreme value.When the objective function of the optimization is harmonic function,the two-dimensional optimization can be simplified as a one-dimensional optimization on the boundary of its feasible region.At last,three examples were given to show the feasibility of the method here.The research ideas and the conclusions can be generalized to the solution of the three-dimensional optimization problems.

Keywords

• Two-dimension optimization problem;Harmonic function;Feasible region boundary;Maximum;One-dimensional search