Quasi $$\epsilon $$ϵ -solutions in a semi-infinite programming problem with locally Lipschitz data

摘要: Under the fulfilment of limiting constraint qualification, a necessary condition for quasi $$\epsilon $$-solution to semi-infinite programming problem (SIP) by means employing some advanced tools variational analysis and generalized differential is established. Sufficient conditions such are also investigated in light convex functions defined terms subdifferential locally Lipschitz functions. Finally, Wolfe type dual model approximate form formulated, weak, strong converse-like duality theorems proposed. Besides, we give simple examples illustrate obtained results.