1) multiobjective variational problem
多目标变分问题
1.
For a class of multiobjective variational problems containing arbitrary norms and Wolfe and Mond Weir type duals problems,under (F ρ) convexity assumptions on the objective and constraint functions involved, the weak and strong duality theorems are proved.
对一类包含任意范数的多目标变分问题(P)及其Wolfe和Mond-Weir型对偶,在对目标和约束函数的(F-ρ)-凸的假设下,证明了弱对偶和强对偶定理。
2.
Considering the Wolfe type and Mond Weir type duals for a class of multiobjective variational problems discussed in paper 1 ,a general dual of such a multiobjective variational problem was proposed,and the corresponding weak and strong duality theorems with respect to properly efficient solutions were proved.
考虑文章〔1〕讨论的一类多目标变分问题的Wolfe型和Mond-Weir型对偶,对这样一类多目标变分问题提出一种一般对偶,鉴于在建立对偶问题时,如果把Geofrion参数作为变量,讨论关于真有效解的对偶性定理存在许多问题,对于预定的Geofrion参数,证明了关于真有效解的相应弱对偶定理和强对偶定
2) nondifferentiable multiobjective variational problem
不可微多目标变分问题
3) Multiobjective variational control problem
多目标变分控制问题
5) multi-objective problem
多目标问题
1.
This paper studies hybrid multiple attribute decision making problem with real numbers and interval numbers and triangle fuzzy numbers,and an unknown weight information on indexes,and affiliate degree model is put forward,then the multi-objective problem is transformed into single-objective problem,and the ranking of alternatives is expressed by affiliate degree.
研究了指标权重未知,指标值为实数、区间数、三角模糊数三种数据类型同时存在的混合型多属性决策问题,提出了从属度方法,把多目标问题转化为单目标问题,根据从属度大小对各方案进行排序。
2.
This paper discusses uncertain multiple attribute decision making problem with real numbers and interval numbers and triangle fuzzy numbers, and affiliate degree model is put forward, then the multi-objective problem is transformed into single-objective problem, and the ranking of alternatives is expressed by affiliate degree.
本文讨论了属性值为实数、区间数、三角模糊数三种数据类型的混合型多属性决策问题,提出了从属度方法,把多目标问题转化为单目标问题,利用从属度对各方案进行捧序。
6) Multi-objective Fractional Programming
多目标分式规划问题
1.
Optimality Condition and Duality Results for a Class of Multi-objective Fractional Programming Problems with Generalized Convexity;
广义凸性条件下一类多目标分式规划问题的最优性条件和对偶
补充资料:变分问题
变分问题
variations! problem
功,,(t},x(t,))二o,沙。(tZ,x(tZ))二o少 p二l,一,r,J二1,‘’‘,q给出,只n十l一>O或n十l一q>0,则曲线端点可沿着相应的n+1一r维或n+1一q维流形运动.在极值曲线的端点横截性条件(transversallty con-改ion)必须满足;这条件与条件〔,)一起,使得可以得到导致某个边值问题的关系式的封闭系统.这边值问题的解有任意常数,这些常数出现在Euler方程的通积分中. 变分问题和多元函数求极值问题的性质之不同在于这样的事实,在前者情形不是在有限维空间中寻找一个点,而是寻找一个函数(或一个无穷维空间中的点).H.E.BanH,pe‘,众撰变分问题「varia石以‘脚心曰;,卿a。,o。。a,3叭a,aJ l)具有固定端点的变分问题(varia山翻prob】emwith爪ed ends)是变分学(variational caleulus)中这样一个问题,其中给出极值的曲线的端点是固定的.例如,在变分学的最简问题中,带有固定端点的inf了{::,,粼F(。,、,*)d:所求的曲线二(t)应通过的起点和终点x(艺。)二x。,欠(艺l)二x.是给定的.由于最简问题的Euler方程(Euler叫Uation)的一般解依赖于两个任意常数,x“x(t,c,,cZ),给出极值的曲线将在对应的边值问题的解中寻找.结果,该边值问题可以有唯一解,多于一个解或根本没有解. 2)具有自由(可移动)端点的变分问题(varia·tional probhm witll free(mob口e)ends)是变分学中这样一个问题,其中给出极值的曲线的端点可沿给定流形运动.例如,如果在压血a问题(BO恤probkm)中所寻找曲线x二(x.(t),二,义。(t”要满足的边界条件数目严格地小于Zn十2: 价,(t、,x(t、),tZ,x(t:))=o,“=l,“‘, p<2“+2,(*)则曲线端点可沿着(Zn十2一p)维流形(‘)运动.如果边界条件(*)以形式
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