在凸過程中的線性算子

Linear Selections From Convex Process

莊茜榕(Chien-Jung Chuang)

指導教授 ： 李金城

中原大學/理學院/應用數學研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400457

摘要

在1950到1980年，有許多連續選擇定理和測度選擇定理被發表出來([5],[7],[8],[9])，其中較著名的成果被應用在動力系統、鑑別性包含、數理經濟和最佳化…等等。([1],[2],[3],[6])
在1967年Rockafellar介紹convex process這個名詞[10]，它扮演和linear operator相類似的角色。在本篇論文中，研究的是在凸過程中的線性算子的基本定理和証明它的存在性，第二單元中，我們會給定集合值函數和凸過程的基本專有名詞並列出使用到的基本性質，第三單元，我們會針對在凸過程中的線性算子的存在性建立一個充份條件。

關鍵字

線性算子

並列摘要

In 1950~1980, many continuous selection theorems and measurable selection theorems were established ([5],[7],[8],[9]) and then some of these famous results were studied and applied to dynamic system, differential inclusion, mathematical economics, optimization … etc.([1],[2],[3],[6])
Convex processes were introduced by Rockafellar in 1967[10] and has been playing an analogous role with linear operators. In this paper, we investigate some basic properties and then prove an existence theorem for a linear selection from a convex process. In Section 2, we give the elementary terminologies of set-valued maps and convex processes and show the basic properties that we are going to use. In Section 3, we establish a sufficient condition for the existence of linear selections from convex processes.

並列關鍵字

selection ； convex process

參考文獻

[1] AUBIN, J.-P. (1979) Mathematical methods of game and economic theory, North-Holland (Studies in Math-ematics and its Applications, Vol.7,1-619)

[5] IOFFE, A.D. (1978) Survey of measurable selection theorems: Russian literature supplement, SIAM J. Contr. Opt., 16, 728-723

[6] KLEIN, E. and A.C, THOMPSON, Theory of Correspondences (1984), by John Wiley Sons. Inc.

[7] MICHAEL, E. (1956) Continuous selections I, Annals of Math.,63,361-381

[8] MICHAEL, E. (1956) Continuous selections Ⅱ, Annals of Math.,64,562-580