Transformation of Nonlinear Programming Problems into Separable ones Using Multilayer Neural Networks
In this paper we present a novel method for transforming nonseparable nonlinear programming (NLP) problems into separable ones using multilayer neural networks. This method is based on a useful feature of multilayer neural networks, i.e., any nonseparable function can be approximately expressed as a separable one by a multilayer neural network. By use of this method, the nonseparable objective and (or) constraint functions in NLP problems can be approximated by multilayer neural networks, and therefore, any nonseparable NLP problem can be transformed into a separable one. The importance of this method lies in the fact that it provides us with a promising approach to using modified simplex methods to solve general NLP problems.
Keywordsseparable nonlinear programming linear programming multilayer neural network
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- M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd Edition, John Wiley & Sons, Inc. (1993).Google Scholar
- C. E. Miller, The Simplex Method for Local Separable Programming, in: Recent Advances in Mathematical Programming, R. L. Graves and P. Wolfee eds., McGraw-Hill (1963), pp89–100.Google Scholar
- M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, in: Lecture Notes in Mathematics No. 630 (1978), G. A. Waston ed., Springer-Verlag, Berlin.Google Scholar