
MONOTONICITY IN STEEPEST ASCENT ALGORITHMS FOR POLYHEDRAL LCONCAVE FUNCTIONSMONOTONICITY IN STEEPEST ASCENT ALGORITHMS FOR POLYHEDRAL LCONCAVE FUNCTIONSAA00703935 
"/Fujishige, Satoru/"Fujishige, Satoru ,
"/Murota, Kazuo/"Murota, Kazuo ,
"/Shioura, Akiyoshi/"Shioura, Akiyoshi
58
(
5
)
, pp.184

208 , 20150623
ISSN:04534514
NCID:AA00703935
Description
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 Lconcave 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 Lconcave functions. The objective of this paper is to show some monotonicity properties of the steepest ascent algorithm for polyhedral Lconcave 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 \Lnatconcave functions.
FullText
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