Search Results 1-20 of 31

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  • Greedy systems of linear inequalities and lexicographically optimal solutions

    Fujishige Satoru

    … The present note reveals the role of the concept of greedy system of linear inequalities played in connection with lexicographically optimal solutions on convex polyhedra and discrete convexity. …

    RAIRO - Operations Research 53(5), 1929-1935, 2019-11


  • A Development of Evolutionary Many-objective Optimization Method for Decision Aid on Distribution System Reconfiguration  [in Japanese]

    Sekizaki Shinya , Yamasaki Takuya , Nishizaki Ichiro , Hayashida Tomohiro , Ishikawa Hiroyuki , Uenishi Hirokazu

    … Since the distribution network reconfiguration problem in the real world has many objectives including discrete objectives, non-convexity, and severe constraints, the distribution system operators have difficulty in finding a preferred solution by him/her with little effort. …

    IEEJ Transactions on Power and Energy 138(12), 925-938, 2018



    Hirai Hiroshi

    … <p>In this paper, we study classes of discrete convex functions: submodular functions on modular semilattices and L-convex functions on oriented modular graphs. … We clarify the relationship to other discrete convex functions, such as <i>k</i>-submodular functions, skew-bisubmodular functions, L<sup>♮</sup>-convex functions, tree submodular functions, and UJ-convex functions. …

    Journal of the Operations Research Society of Japan 61(1), 71-109, 2018



    Shioura Akiyoshi

    … <p>L-convexity is a concept of discrete convexity for functions defined on the integer lattice points, and plays a central role in the framework of discrete convex analysis. …

    Journal of the Operations Research Society of Japan 60(3), 216-243, 2017


  • Robust Projective Template Matching

    ZHANG Chao , AKASHI Takuya

    … Estimating the projective transformation remains a difficult problem due to high-dimensionality and strong non-convexity. … Our approach is to quantize the parameters of projective transformation with binary finite field and search for an appropriate solution as the final result over the discrete sampling set. …

    IEICE Transactions on Information and Systems E99.D(9), 2341-2350, 2016


  • Congestion games viewed from M-convexity

    Fujishige Satoru , Goemans Michel , Harks Tobias , Peis Britta , Zenklusen Rico

    … We show that the fast convergence of best-response sequences results from M-convexity (of Murota (1996)) of the potential function associated with the game. …

    Operations Research Letters 43(3), 329-333, 2015-04-17



    Murota Kazuo

    … In discrete convex analysis, L-convexity and M-convexity are defined for functions in both discrete and continuous variables. … Polyhedral L-/M-convex functions connect discrete and continuous versions. … Specifically, polyhedral L-/M-convex functions with certain integrality can be identified with discrete versions. …

    Journal of the Operations Research Society of Japan 58(3), 291-305, 2015



    Shioura Akiyoshi , Tamura Akihisa

    … Since then, several variants of gross substitutes condition as well as a discrete concavity concept, called M<sup>♮</sup>-concavity, have been introduced to show the existence of an equilibrium in various models. …

    Journal of the Operations Research Society of Japan 58(1), 61-103, 2015


  • Bisubmodular polyhedra, simplicial divisions, and discrete convexity

    Fujishige Satoru

    … We consider a class of integer-valued discrete convex functions, called BS-convex functions, defined on integer lattices whose affinity domains are sets of integral points of integral bisubmodular polyhedra. … We examine discrete structures of BS-convex functions and give a characterization of BS-convex functions in terms of their convex conjugate functions by means of (discordant) Freudenthal simplicial divisions of the dual space. …

    Discrete Optimization (12), 115-120, 2014-05


  • A Brief Introduction to Machine Learning with Submodular Functions and Recent Trends  [in Japanese]

    KAWAHARA Yoshinobu

    … Submodularity is known to be an analogous concept for a set function of convexity in a continuous function. … Recently, it has been used as the mathematical basis for developments of fast algorithms or analyses of discrete problems in machine learning. …

    電子情報通信学会技術研究報告. IBISML, 情報論的学習理論と機械学習 113(476), 87-88, 2014-02-27

  • Legendre duality in combinatorial study of matrix pencils

    MUROTA Kazuo

    Japan Journal of Industrial and Applied Mathematics 29(2), 205-236, 2012-06-01

    References (25) Cited by (1)

  • Recent Development of Intelligent Information Processing with Submodularity(<Special Issue>Discrete Structure Manipulation Systems-The Art of Algorithms for Intelligent Information Processing)  [in Japanese]

    KAWAHARA Yoshinobu , NAGANO Kiyohito , WASHIO Takashi , Yoshinobu Kawahara , Kiyohito Nagano , Takashi Washio

    人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 27(3), 252-260, 2012-05-01

    JSAI  References (66)

  • Prismatic Algorithm for Discrete D.C. Programming Problem  [in Japanese]

    KAWAHARA Yoshinobu , WASHIO Takashi

    … In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. … The developed algorithm is a branch-and-bound-based algorithm which responds to the structure of this problem through the relationship between submodularity and convexity. …

    電子情報通信学会技術研究報告 : 信学技報 111(275), 93-98, 2011-11-09

  • Information-Maximization Clustering : Analytic Solution and Model Selection

    SUGIYAMA Masashi , YAMADA Makoto , KIMURA Manabu , HACHIYA Hirotaka

    … A notable advantage of this approach is that it only involves continuous optimization of a logistic model, which is substantially easier than discrete optimization of cluster assignments. … However, this method still suffers from two weaknesses: (i) manual tuning of kernel parameters is necessary, and (ii) finding a good local optimal solution is not straightforward due to the strong non-convexity of logistic-regression learning. …

    IEICE technical report 110(476), 69-76, 2011-03-21

    References (14)

  • 306 Procurement-Inventory System Based on Discrete Convex Analysis  [in Japanese]

    MORIGUCHI Satoko , TSUCHIMURA Nobuyuki

    … Our application is based on the fact that the inventory cost function has L^#-convexity, which is an inportant concept of discrete convexity in the theory of optimization. …

    The Proceedings of Manufacturing Systems Division Conference 2010(0), 57-58, 2010


  • Submodular Cost Set Cover Problem


    … We give approximation algorithms for these problems exploiting the discrete convexity of submodular functions. …

    情報処理学会研究報告. AL, アルゴリズム研究会報告 126, C1-C8, 2009-09-15

    References (34)

  • Optimization algorithms based on discrete convexity  [in Japanese]

    森口 聡子

    産業技術大学院大学紀要 (2), 183-192, 2008

  • A Note on Discrete Convexity and Local Optimality

    UI Takashi

    … This paper explores the discrete analogue of this property. … We consider arbitrary locality in a discrete space and the corresponding local optimum of a function over the discrete space. … We introduce the corresponding notion of discrete convexity and show that the local optimum of a function satisfying the discrete convexity is also a global optimum. …

    Japan Journal of Industrial and Applied Mathematics 23(1), 21-29, 2006-02-01

    IR  References (14)

  • An Optimal Solution Algorithm for Order Frequency Problems in a Discrete EOQ Model  [in Japanese]

    YOSHIKAWA Shin'ichi , TANAKA Masatoshi , TABATA Yoshio

    … In actual inventory problems, it is desirable that item order frequencies are obtained as discrete integers. …

    Journal of Japan Industrial Management Association 57(1), 32-38, 2006

    J-STAGE  References (11)

  • Scaling Algorithms for M-Convex Function Minimization

    MORIGUCHI Satoko , MUROTA Kazuo , SHIOURA Akiyoshi

    … M-convex functions have various desirable properties as convexity in discrete optimization. …

    IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, A 85(5), 922-929, 2002-05-01

    References (26) Cited by (2)

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