On logarithmic smoothing of the maximum function

被引:0
|
作者
Vazquez, FG [1 ]
Günzel, H
Jongen, HT
机构
[1] Univ Americas Puebla, Dept Math & Phys, Cholula 72820, Mexico
[2] Rhein Westfal TH Aachen, Dept Math C, D-52056 Aachen, Germany
关键词
maximum function; logarithmic barrier function; interior approximation; stationary point; Morse index;
D O I
暂无
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We consider the maximum function f resulting from a finite number of smooth functions. The logarithmic barrier function of the epigraph of f gives rise to a smooth approximation g(epsilon) of f itself, where epsilon > 0 denotes the approximation parameter. The one-parametric family g(epsilon) converges - relative to a compact subset - uniformly to the function f as epsilon tends to zero. Under nondegeneracy assumptions we show that the stationary points of g(epsilon) and f correspond to each other, and that their respective Morse indices coincide. The latter correspondence is obtained by establishing smooth curves x(epsilon) of stationary points for g(epsilon), where each x(epsilon) converges to the corresponding stationary point of f as epsilon tends to zero. In case of a strongly unique local minimizer, we show that the nondegeneracy assumption may be relaxed in order to obtain a smooth curve x(epsilon).
引用
收藏
页码:209 / 220
页数:12
相关论文
共 50 条