簡易檢索 / 詳目顯示

回結果列表
研究生： 蘇宏恭
Su, Hung-Kung
論文名稱： 關於一維Monge-Kantorovich問題的一些研究
Some analysis on one-dimensional Monge-Kantorovich's problem
指導教授： 陳國璋
Chen, Kuo-Chang
口試委員: 蔡東和
Tsai, Dong-Ho
陳建隆
Chern, Jann-Long
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2012
畢業學年度： 100
語文別： 英文
論文頁數： 48
中文關鍵詞： 優化運輸問題 、優化 、最佳
外文關鍵詞： Monge-Kantorovich, spatial economics, trnsportation, optimal map, network flow optimization, convex programming
相關次數： 點閱：2  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 在本篇論文中，為了了解Monge-Kantorovich's 問題，我們考慮一些基本的成本函數來研究一維的運輸問題。我們也考慮一類一維特殊例子，滿足連續分部的邊界條件mu與nu及片段連續的成本函數c，然後應用雙隨機矩陣去得到數值最佳估計。

    In order to better understand the Monge-Kantorovich's problem, in this thesis we study some elementary examples of cost functions for the one dimensional transportation problem. We also consider a special case of the problem with marginals ,  that are continuously distributed on the line with piecewise continuous cost functions c of distance, and then use doubly stochastic matrices associated to mu and nu  to obtain numerical estimates of the optimal transportation cost.

    1 Basic continuous cost functions of distance 2 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Cyclical monotonicity and Kantorovich duality . . . . . . . . . . . . . . . . . . . . . 4 1.3 An estimate of optimal transportation cost with continuous cost function on the line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Exact solutions to the transportation problem on the real line 19 2.1 The no-crossing rule for concave costs . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Networks and the transportation hierarchy . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Convex separable flow optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3 Wasserstein distances 37 3.1 Topological properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 on real line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4 Appendix 42 4.1 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    [1] Ambrosio, L. Lecture notes on optimal transport problems. In Mathematical aspects of
    evolving interfaces (Funchal, 2000), vol. 1812 of Lecture Notes in Math. Springer, Berlin,
    2003, pp. 152.
    [2] Cedric Villani. Topics in optimal transportation Providence, RI : American Mathematical
    Society, c2003.
    [3] Cedric Villani. Optimal transport, old and new Berlin, Heidelberg : Springer Berlin
    Heidelberg, 2009.
    [4] Erdelyi, A. & Etherington, I. M. H. 1940 Some problems of non-associative combinations
    (2).Edinb. Math. Notes 32, 7-12.
    [5] Gangbo, W. & McCann, R. J. 1996 The geometry of optimal transportation. Acta Math.
    177, 113-161.
    [6] Giuseppe Buttazzo, Eugene Stepanov, Aldo Pratelli, Sergio Solimini, Optimal urban
    networks via mass transportation, Berlin : Springer, c2009.
    [7] Kantorovich, L. 1942 On the translocation of masses. C. R. (Dokl.) Acad. Sci. URSS
    (N.S.) 37, 199-201.
    [8] Kellerer, H. G. 1984 Duality theorems for marginal problems. Z. Wahrsch. Verw. Gebiete
    67, 399-432.
    [9] Koopmans, T. C. 1949 Optimum utilization of the transportation system. Econometrica
    (Suppl.) 17, 136-146
    [10] Marc Bernot, Vicent Caselles, Jean M. Morel, Optimal transportation networks : models
    and theory, Berlin New York : Springer-Verlag, c2009.
    [11] McCann, R. J. Exact solutions to the transportation problem on the line. R. Soc. Lond.
    Proc. Ser. A Math. Phys. Eng. Sci., 1999, 455, 1341-1380
    [12] Monge, G. 1781 Memoire sur la theorie des deblais et de remblais. Histoire de l'Academie
    Royale des Sciences de Paris, avec les Memoires de Mathematique et de Physique pour
    la m^eme annee, pp. 666-704.
    [13] Vasershtein, L. N. Markov processes over denumerable products of spaces describing
    large system of automata. Problemy Peredaci Informacii 5, 3 (1969), 64-72.

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE