(h,φ)-η subgradient and its application to non-smooth(h,φ)-semi-infinite programming problems
Jianming Huang · 2009
At first,with the Ben-Tal generalized algebraic operations,the notion of(h,φ)-η directional derivative is introduced,and relative basic properties are discussed.Then,with the notion of(h,φ)-η directional derivative,(h,φ)-η subgradient and generalized regular weakly(h,φ)-Lipschitz function are defined,and some basic properties are discussed.In the end,with the alterlative theorm on(h,φ)-η pre-invex function and(h,φ)-η prequasi-linear function,the optimality conditions of non-smooth(h,φ)-semi-infinite programming problem are discussed and a constraint qualification of(h,φ)-Kuhn-Tucker conditions are gotten.