Constrained Generalized Equation Of Composite Convex Metric Regularity,

Constraint optimization problem plays an important role in mathematical pro-gramming. This paper mainly concerns a convex-composite generalized constraint equation in Banach spaces and Asplund spaces. Using variational analysis technique, we establish sufficient and necessary conditions for such an equation to be metrically subregular in terms of normal cones and coderivatives. Moreover, we provide some characterizations for Clarke tangent derivative of convex-composite functions to be metrically subregular.