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    A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers
October  2006, 2(4): 373-385. doi: 10.3934/jimo.2006.2.373

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, Australia

Received  November 2005 Revised  April 2006 Published  October 2006

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.
Keywords: Interval number, Multi-objective programming., Interval order relation, Linear and nonlinear programming.
Mathematics Subject Classification: 65G30, 90C70, 90C30, 49M3.
Citation: Bao Qing Hu, Song Wang. A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions. Journal of Industrial & Management Optimization, 2006, 2 (4) : 373-385. doi: 10.3934/jimo.2006.2.373
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