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