广义拟可微函数的微分

摘要

本文给出一种广义拟可微函数类,它是Demyanov与Rubinov(1980)意义下拟可微函数的推广.通过凸集类对的空间的某些理论,建立了这类广义拟可微函数的微分学理论,包括加法运算、数乘运算、乘法运算、除法运算、极大值运算,极小值运算以及复合运算的微分公式和中值定理.这些结果为广义拟可微类函数优化研究提供了基本工具.%A class of generalized quasi-differentiable functions, as an extension of the class of quasi-differentiable functions in the sense of Demyanov and Rubinov(1980), is studied systematically in this paper. Based on the theory of the space of pairs of convex-set collections proposed by[17], the calculus theory of generalized quasi-differential is established, including the operations of scalar multiplication, multiplication, division, pointwise maximum, pointwise minimum and composition. And several mean-value theorems are demonstrated as well. The proposed calculus theory provides a foundation for the study on generalized quasi-differentiable optimization.