摘要
1744年 Leonhard Euler 曾說過：就是因為整個宇宙的形狀幾乎是完美無缺的，而且事實上聰明的造物者〈神〉設計在沒有任何東西的世界上，設法把沒有最大或最小的規則照亮在後。[摘錄自BORIS S. MORDUKHOVICH 所著作多變數分析和廣義的微分I書中前言]這就是我研究寫出本文的動機。 這篇論文分為三個部分。第一部分將探討 Gateaux 微分的定義和証明一些定理及給一些的應用。第二部分敘述 Frechet 微分的定義和定理及性質的証明。 最後，介紹共軛(對偶)函數(conjugate function)和劣微分(subdifferential)的定義、定理及應用。
並列摘要
In 1744, Leonhard Euler said that ”Namely, because the shape of the whole universe is most perfect and, in fact, designed by the wisest creator, nothing in all of the world will occur in which no maximum or minimum rule is somehow shining forth.” [BORIS S. MORDUKHOVICH-Variational Analysis and Generalized Differ-entiation I]. It motivates me to study in this field. This thesis is divided to three parts. In the first part, we study the definition of Gateaux derivative (G.D.) and prove some theo- rems and give some applications. In the second part, we state the definition of F´rech˙et derivative (F.D.) and prove some theorems, properties and proposition. Finally, we introduce the definitions of conjugate function and subdifferential, with some applications.
參考文獻
延伸閱讀
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