In this paper the authors study the following parametric nonsmooth optimization problem with parameter vector u∈ℝp: minimize f(x) subject to g(x)+u∈¸-K, x∈C where f:E∈ℝ and g:E∈ℝp are locally Lipschitzian mappings, C is a nonempty closed subset of a Banach space E, and K is a convex cone in ℝp. Optimization problems with a finite number of inequality and equality constraints and with right-hand perturbations belong to the class of problems (Pu). For each parameter vector u∈ℝp we can associate the global optimal value p(u)∈ℝpℝ∈¸-∈,∈∈ for (Pu) defined as p(u):¸=inf∈f(x):g(x)+u∈¸-K and x∈C∈, with the convention p(u)=¸+∈ is infeasible. The optimal solutions set will be denoted S(u).
