Global Optimization for the Sum of Certain Nonlinear Functions

Abstract

We extend work by Pei-Ping and Gui-Xia, 2007, to a global optimization problem for more general functions. Pei-Ping and Gui-Xia treat the optimization problem for the linear sum of polynomial fractional functions, using a branch and bound approach. We prove that this extension makes possible to solve the following nonconvex optimization problems which Pei-Ping and Gui-Xia, 2007, cannot solve, that the sum of the positive (or negative) first and second derivatives function with the variable defined by sum of polynomial fractional function by using branch and bound algorithm.

A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

“…In the previous our work [15], we treat the same problem ( ) applying Pei-Ping and Gui-Xia's [5]. The method needs to add the new valuables and takes a long time to solve the optimal problem.…”