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Converting general nonlinear programming problems into separable programming problems with feedforward neural

Bao-Liang Lu1, Koji Ito

  • 1Department of Computer Science and Engineering, Shanghai Jiao Tong University, 1954 Hua Shan Road, 200030 Shanghai, People's Republic of China. blu@cs.sjtu.edu.cn

Neural Networks : the Official Journal of the International Neural Network Society
|December 25, 2003
PubMed
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This study introduces a novel method using feedforward neural networks (FNNs) to convert general nonlinear programming (NLP) problems into separable programming (SP) problems, simplifying complex optimization tasks.

Area of Science:

  • Optimization Theory
  • Computational Mathematics
  • Artificial Intelligence

Background:

  • Nonlinear programming (NLP) problems often involve complex, nonseparable functions that are difficult to solve.
  • Existing transformation techniques for NLP to separable programming (SP) have limitations in generality and applicability.
  • Feedforward neural networks (FNNs) offer powerful function approximation capabilities.

Purpose of the Study:

  • To present a general method for converting arbitrary nonlinear programming (NLP) problems into separable programming (SP) problems.
  • To leverage the approximation and decomposition properties of feedforward neural networks (FNNs) for this conversion.
  • To demonstrate the advantages of the proposed method over existing transformation techniques.

Main Methods:

Related Experiment Videos

  • Utilizing feedforward neural networks (FNNs) to approximate nonseparable objective functions and constraints in NLP problems.
  • Transforming NLP problems into equivalent SP problems by expressing nonlinearities as compositions of single-variable functions.
  • Analyzing the computational complexity and comparing the proposed method with existing approaches.

Main Results:

  • The proposed FNN-based method offers greater generality compared to existing NLP to SP transformation techniques.
  • This method enables the formulation of SP problems even when the analytical form of objective functions or constraints is unknown.
  • The resulting SP problems facilitate the selection of grid points for piecewise linear approximation.

Conclusions:

  • Feedforward neural networks provide a powerful and general tool for converting complex NLP problems into more tractable SP problems.
  • The method enhances the applicability of optimization techniques to problems with unknown or complex nonlinearities.
  • The conversion to SP problems simplifies subsequent solution processes, such as using the simplex method.