The Two Descending Dimension Methods For Nonlinear Programing Problem

This paper discussed two descending dimension methods which can solve nonlinear global optimization problem combined with filled function method and accelerated single variable method. The details are as follows:(1) Chapter 1 introduced the basic theory of the global optimization problem and the main work of this paper. The global optimization problem was classified based on the target function and restraint conditions of global optimization problem. The paper also introduced the base definition and theorem of the global optimization problem.(2) Chapter 2 described a filled function method based on dimensionality reduction. The filled function was an effective auxiliary function to solve global optimization problem. The greatest strength of the filled function method was that it can help us to find another better local optimal solution from a local optimal solution. Meanwhile, the transformation function which used descending dimension method can convert the n-dimension box-constrained problem to a one-dimensional problem defined at interval [0, π]. Moreover, Chapter 2 put forward specific descending dimension method and proposed a new filled function. Also, Chapter 2 provided a definition of one-dimensional filled function, analysed and proved the properties of the filled function. Chapter 2 offered theoretical algorithm and algorithm descriptions, proved the feasibility of the algorithm through numerical experiment.(3) Chapter 3 described the improved descending dimension method based on the Chapter 2 and combined with the accelerated single variable method, proposed a new algorithm which can more efficient apply to higher dimensional analysis examples. This chapter constructed the limited range of dimension reduction transformation, presented the domain definition of one-dimensional objective function. Put forward the accelerated single variable method, this method directly used the properties of objective function in the domain, demarcated interval and constructed auxiliary function to find out the optimal solution instead of selection the local optimal value.