学術雑誌論文 MONOTONICITY IN STEEPEST ASCENT ALGORITHMS FOR POLYHEDRAL L-CONCAVE FUNCTIONS

Fujishige, Satoru  ,  Murota, Kazuo  ,  Shioura, Akiyoshi

58 ( 5 )  , pp.184 - 208 , 2015-06-23
ISSN:0453-4514
NII書誌ID(NCID):AA00703935
内容記述
For the minimum cost flow problem, Hassin (1983) proposed a dual algorithm, which iteratively updates dual variables in a steepest ascent manner. This algorithm is generalized to the minimum cost submodular flow problem by Chung and Tcha (1991). In discrete convex analysis, the dual of the minimum cost flow problem is known to be formulated as maximization of a polyhedral L-concave function. It is recently pointed out by Murota and Shioura (2014) that Hassin's algorithm can be recognized as a steepest ascent algorithm for polyhedral L-concave functions. The objective of this paper is to show some monotonicity properties of the steepest ascent algorithm for polyhedral L-concave functions. We show that the algorithm shares a monotonicity property of Hassin's algorithm. Moreover, the algorithm finds the “nearest” optimal solution to a given initial solution, and the trajectory of the solutions generated by the algorithm is a "shortest" path from the initial solution to the "nearest" optimal solution. The algorithm and its properties can be extended for polyhedral \Lnat-concave functions.
本文を読む

http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/198549/1/jorsj.58.184.pdf

このアイテムのアクセス数:  回

その他の情報