In certain case it might be necessary to further decompose a spiral into convex subsets . 在某些情況下,把一個(gè)螺旋形進(jìn)一步分解成凸子集是必要的。
A relatively optimal compact convex subset of continuous games 連續(xù)對(duì)策的相對(duì)最優(yōu)緊凸策略子集
The maximal value point s problem of a convex function on a closed convex subset in locally convex space is considered by using the level set of function , - subdifferential and - normal cone . it gives several equivalent characters on the optimal solutions of the problem 利用函數(shù)的水平集, -次微分和-法向錐等工具研究局部凸空間的凸函數(shù)在閉凸子集上的最大值點(diǎn)問(wèn)題,給出了最優(yōu)解的幾個(gè)等價(jià)刻劃
Throughout the following of this section , e denotes a real banach space and p is a cone in e . in chapter , a new three - solution theorem is obtained . moreover , the famous amann ' s and leggett - williams " three - solution theorems in nonlinear functional analysis can be seen as its special cases , namely they are united . so they are improved . the main results can be stated as the following : let d be a nonempty bounded close convex subset in e , and nonnegative continuous functional on d . and is concave while is convex . suppose 0 < d and denote 首先我們約定,在下文中, e是實(shí)banach空間, p是e中的錐。在第一章中,我們利用錐理論與不動(dòng)點(diǎn)指數(shù)理論統(tǒng)一了著名的amann三解定理與leggett - williams三解定理。主要結(jié)論是:設(shè)d是e中的非空有界閉凸集, ,是d上的非負(fù)連續(xù)泛函,且是凹泛函,是凸泛函。