Paper Info
Title
Converting general nonlinear programming problems into separable programming problems with feedforward neural networks.
Abstract
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques; (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown; (c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems.
Year
DOI
Venue
2003
10.1016/S0893-6080(02)00234-4
Neural Networks
Keywords
DocType
Volume
separable programming,nonlinear function,nonlinear programming,piecewise linear approximation,general nonlinear programming problem,nonseparable objective function,separable function,precise analytic objective function,simplex method,feedforward neural network,separable programming problem,approximate arbitrary continuous nonlinear,general nonlinear programming,existing transformation approach,sp problem,nlp problem,computational complexity,objective function,optimization problem
Journal
16
Issue
ISSN
Citations 
7
0893-6080
0
PageRank 
References 
Authors
0.34
9
2
Name
Order
Citations
PageRank
Bao-Liang Lu12361182.91
Koji Ito2154.52