Abstract: The optimality conditions of the constraint nonsmooth programming problem are discussed on R, under γ-vexity assumptions, by using γ-subdifferen tiation. The theorem of the local minimum of γ-vex function must be the global minimum is proven, and necessary conditions and optimality sufficient conditions of constraint nonsmooth programming are given。

Key words: γ-subdifferentiation, γ-vex, nonsmooth programming, optimality condition