A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions

Bao Qing Hu; Song Wang

doi:10.3934/jimo.2006.2.373

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2006, Volume 2, Issue 4: 373-385. Doi: 10.3934/jimo.2006.2.373

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A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions

Bao Qing Hu^1, and
Song Wang^2,

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072
2.
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009

Received: October 31, 2005

Revised: March 31, 2006

Published: September 2006

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Abstract

In this paper we present a novel approach to a class of constrained nonlinear programming problems with interval objective functions. In this approach we first introduce a new concept of optimal solutions to the nonlinear programming problem, based on a new linear order relation for interval numbers proposed in Part 1 of this series. We then propose two efficient methods for the solution of the nonlinear optimization problem with respect to the new interval order relation. Comparisons between our approach and some existing methods will be given using illustrative examples. The numerical results show the superiority of our method to the existing ones.

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Mathematics Subject Classification: 65G30, 90C70, 90C30, 49M37.

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