Success Guarantee of Dual Search in Integer Programming: p-th Power Lagrangian Method

Authors:
D. Li;X. L. Sun
Affiliations:
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong email: dli@se.cuhk.edu.hk/ Department of Mathemati ...;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong Department of Mathematics, Shanghai University, Baoshan, Shanghai 200436, ...
Venue:
Journal of Global Optimization
Year:
2000

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Abstract

Although the Lagrangian method is a powerful dual search approach in integer programming, it often fails to identify an optimal solution of the primal problem. The p-th power Lagrangian method developed in this paper offers a success guarantee for the dual search in generating an optimal solution of the primal integer programming problem in an equivalent setting via two key transformations. One other prominent feature of the p-th power Lagrangian method is that the dual search only involves a one-dimensional search within [0,1]. Some potential applications of the method as well as the issue of its implementation are discussed.