Quasidifferentiability of nonsmooth quasiconvex functions

The paper deals with nonsmooth quasiconvex functions and develops a quasidifferential analysis for this class of functions. Therefore, in terms of sub and superdifferentials, first order approximations of the functions are derived, optimality conditions are stated and directions of descent (either simple feasible or of steepest descent) are determined. Moreover, a relation among positively homogeneous convex and quasiconvex functions is established