Abstract
The phrase convex optimization refers to the minimization of a convex function over a convex set. However the feasible convex set need not be always described by convex inequalities. In this article we consider a convex feasible set which is described by inequality constraints that are locally Lipschitz and not necessarily convex or differentiable. We show that if the Slater constraint qualification and a simple non-degeneracy condition is satisfied then the Karush–Kuhn–Tucker type optimality condition is both necessary and sufficient.
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Dutta, J., Lalitha, C.S. Optimality conditions in convex optimization revisited. Optim Lett 7, 221–229 (2013). https://doi.org/10.1007/s11590-011-0410-3
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DOI: https://doi.org/10.1007/s11590-011-0410-3