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Hidden Convex Minimization

✍ Scribed by Duan Li; Zhi-You Wu; Heung-Wing Joseph Lee; Xin-Min Yang; Lian-Sheng Zhang


Publisher
Springer US
Year
2005
Tongue
English
Weight
411 KB
Volume
31
Category
Article
ISSN
0925-5001

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Minimization of an M-convex function
✍ Akiyoshi Shioura πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 343 KB

We study the minimization of an M-convex function introduced by Murota. It is shown that any vector in the domain can be easily separated from a minimizer of the function. Based on this property, we develop a polynomial time algorithm.

A VU-algorithm for convex minimization
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For convex minimization we introduce an algorithm based on VU-space decomposition. The method uses a bundle subroutine to generate a sequence of approximate proximal points. When a primal-dual track leading to a solution and zero subgradient pair exists, these points approximate the primal track poi