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Author: 陳子軒
Chen, Jer-Shain
Thesis Title: 非線性互補問題的軌跡之特性與連續性
Characterization and Continuity of Trajectories For
Advisor: 朱亮儒
Chu, Liang-Ju
Degree: 碩士
Master
Department: 數學系
Department of Mathematics
Academic Year: 84
Language: 中文
Number of pages: 29
Keywords (in Chinese): 二次凸規劃軌跡內點算法最大單調算子單調互補問題
Keywords (in English): convex quadraic programming, trajectory, interior point algorithm, maximal monotone operator, monotone complementarity problem
Thesis Type: Academic thesis/ dissertation
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  • 這篇論文主要是針對在R^n上之非線性單調互補問題建立一些基本的結果.
    整篇文章有兩個主要目的. 首先是刻劃一般凸規劃的解集合的特性, 如引
    理2.1與推論2.6說明了子微分算子在其解集合內是常數函數, 定理2.2
    與2.7分別將解集合用不同的形式表現出來. 並且我們也提供了一個使這
    解集合有界的充分必要條件, 如定理2.3. 其次, 我們延伸Kojima等人的
    線性結果到非線性的單調互補問題而得到一有界且連續的軌跡並且導出其
    所有的聚點都是原互補問題的解, 如定理3.13與3.14.

    By means of elementary arguments, the paper establishes basic
    results on nonlinaer monotone complementarity problem in R^n
    under a milder condition.In the paper, we focus on two topics.
    We first characterize the solution setof general convex
    programming and provide a sufficient and necessary condition so
    thatthe solution set is bounded. Secondly, we extend the result
    of Kojima et al.to nonlinear monotone complementarity problems
    and obtain that the trajectories are bounded,continuous. As
    well, all the cluster points are solutions of the given
    complementarity problem.
    By means of elementary arguments, the paper establishes basic

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