Calculus rules of generalized $\epsilon-$subdifferential forvector valued mappings and applications
Shengji Li, Xiaole Guo · Journal of Industrial and Management Optimization · 2012
In this paper, a generalized $\epsilon-$subdifferential, which wasdefined by a norm, is first introduced for a vector valued mapping.Some existence theorems and the properties of the generalized$\epsilon-$subdifferential are discussed. A relationship between thegeneralized $\epsilon-$subdifferential and a directional derivativeis investigated for a vector valued mapping. Then, the calculusrules of the generalized $\epsilon-$subdifferential for the sum andthe difference of two vector valued mappings were given. Thepositive homogeneity of the generalized $\epsilon-$subdifferentialis also provided. Finally, as applications, necessary and sufficientoptimality conditions are established for vector optimizationproblems.