Global Optimization Algorithm And Its Application Research

In the field of science, economics and engineering, many problems require the use ofoptimization technique. The algorithm for finding a local solution of a single objectiveoptimization problem is relatively mature. But if the problem has many local solutions, to find itsglobal solution is rather difficulty. Due to the importance of the global optimal solution to realworld problems, the research of this kind of problem is challenging and having importantpractical significance. This dissertation focuses on the latter problem.First of all, this dissertation gives a summary of global optimization methods. Then a newalgorithm named “direction-cut-peak function” method is given in the second chapter. Comparedwith the cut-peak function method, the new method has such advantages: the transition from onelocal minima to another one, a series n dimensional auxiliary optimization problems need to besolved by the cut-peak function method and this needs large computational cost. While thedirection-cut-peak function method solves a series of one-dimensional optimization problems tofind a new descend point and a local minima by solving the original problem. As an applicationof the new method, in the third chapter, we solve the system of nonlinear equations in boxconstraint by transforming it to a nonlinear least square problem. The fourth chapter is asummary of the thesis and prospect.