A DIMENSIONALITY REDUCTION PRINCIPLE ON THE OPTIMIZATION OF FUNCTION

作者：Gao, Chaobang; Wen, Jiajin

来源：Journal of Mathematical Inequalities, 2013, 7(3): 357-375.

DOI：10.7153/jmi-07-32

• optimization
• dimensionality reduction principle
• function power mean
• theta-average gravity norm

In this paper, we put out a dimensionality reduction principle on the optimization of function, in other words, we show that inf(a is an element of Rn+) {f(a)} = 0 only if
K-inf,(a is an element of[0,1]m)k is an element of(m+1) {f(a(1)I(k1),...,a(m),Ikm+1, O-n-k(1) - ... - k(m+1))} = 0
under the proper hypotheses. As applications, we study the optimal problems of linear inequalities involving function power means. In order to show the significance of our results, we give an example for a discrete case by means of the software Mathematica and another example involving space science.

• 出版日期2013-9
• 单位成都大学