Generic Existence of Solutions of Symmetric Optimization Problems

被引：2
|
作者：
Zaslavski, Alexander J. [1 ]
机构：
[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
来源：
SYMMETRY-BASEL | 2020年 / 12卷 / 12期
关键词：
complete metric space; generic element; lower semicontinuos function; uniformity; CONVEX-FUNCTIONS; FIXED-POINTS; POROSITY;
D O I：
10.3390/sym12122004
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper we study a class of symmetric optimization problems which is identified with a space of objective functions, equipped with an appropriate complete metric. Using the Baire category approach, we show the existence of a subset of the space of functions, which is a countable intersection of open and everywhere dense sets, such that for every objective function from this intersection the corresponding symmetric optimization problem possesses a solution.
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页码：1 / 6
页数：6
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