Aggregate Homotopy Method for Min-Max-Min Programming Satisfying a Weak-Normal Cone Condition

Hui Juan Xiong; B. Yu

doi:10.4028/www.scientific.net/AMM.50-51.669

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 50-51Aggregate Homotopy Method for Min-Max-Min...

Aggregate Homotopy Method for Min-Max-Min Programming Satisfying a Weak-Normal Cone Condition

Abstract:

Min-max-min programming is an important but difficult nonsmooth programming. An aggregate homotopy method was given for solving min-max-min programming by Bo Yu el al. However, the method requires a difficult to verify weak-normal cone condition. Moreover, the method is only theoretically with no algorithmic implementation. In this paper, the weak normal cone condition is discussed first. A class of min-max-min programming satisfying the condition is introduced. A detailed algorithm to implement the method is presented. Models arising from some applications such as support vector machine for multiple-instance classification in data mining, can be included in the problem. In the end, the aggregate homotopy method is given to solve the multiple-instance support vector machine model.

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Periodical:

Applied Mechanics and Materials (Volumes 50-51)

Pages:

669-672

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.50-51.669

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Online since:

February 2011

Authors:

Hui Juan Xiong, B. Yu

Keywords:

Aggregate Function, Homotopy Method, Min-Max-Min Programming, Multiple-Instance Classification, Weak-Normal Cone Condition

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References

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