變分不等式解的存在性與特徵

Characterization and existence of solutions to variational inequalities

李明輝(Ming-Fai Lee)

指導教授 ： 朱亮儒

國立臺灣師範大學/理學院/數學系/碩士(1999年)

摘要

在過去數十年間一般變分不等式解的存在性已有快速的發展;而此篇論文的主要內容是在減弱算子和限制集合的條件下對於變分不等式建立一些解的存在性定理及特徵;在第二節中,我們主要是針對在不同形式的Karamardian 條件下,探討參數變分不等式解的存在性;而在第三節中,我們將探討各種不同單調算子在一般變分不等式解集合的特性;最後在有限維空間建立一可應用於數理經濟的等價關係o

關鍵字

變分不等式 ； 參數變分不等式 ； Karamardian 條件 ； 強制條件 ； 極大單調 ； 嚴格單調 ； 強單調 ； 非環多值函數

並列摘要

Existence results are developed for generalized variational inequalities. In addition, we also establish several related characteristics about solutions. This is done by studying a certain parametric family of variational inequality problems.
The treatment covers noncompact convex constraint regions in
locally convex topological vector spaces and upper semicontinuous operators having acyclic images. The main results rely on some coercivity conditions of Karamardian's type for multivalued operators. Further, we establish some interesting equivalent characteristics in the setting Hilbert spaces. In virtue of some kind of monotonicity, those results extend several existence results in the literature
of nonlinear variational inequalities.

並列關鍵字

variational inequality ； parametric variational inequality ； Karamardian condition ； coercive condition ； maximal monotone ； strictly monotone ； strongly monotone ； acyclic multifunction

參考文獻

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functions and variational inequality problems, J. Optim. Theory Appl.104(1) (2000), 59-71.

[3] E.G. Begle , Locally connected spaces and

generalized manifolds, Amer. Math. J. 64 (1942), 553-574.

[4] A. Bensoussan and J.L. Lion, Controle