A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

Mio Horai,Takashi G Nitta,Hideo Kobayashi

doi:10.1155/2016/1304954

Abstract

We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

Highlights

Optimization problems appeared in many subjects [1,2,3], for example, technology [4,5,6,7] and economy [8,9,10]
We propose a specific nonlinear and nonconvex optimization technique for (P)
We found a global ε-optimal value V∗ = 59.3054 when the global ε-optimal solution is (x1, x2)T = (1, 1.6180)

Summary

Introduction

Optimization problems appeared in many subjects [1,2,3], for example, technology [4,5,6,7] and economy [8,9,10]. We propose a specific nonlinear and nonconvex optimization technique for (P). It is generalized by Jiao et al, 2013 [4]. The method needs to add the new valuables and takes a long time to solve the optimal problem. Jiao et al propose the technique which does not launch new ones for the following problems: h0. We obtain the approximate value by Simplex method and Branch and Bound Algorithm [17, 18].

Linear Relaxation Programing

Branch and Bound Algorithm

Algorithm Statement

Convergence of the Optimization Method

Numerical Experiment

Concluding Remarks