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Semilocally prequasi-invex functions and characterizations
In this paper, based on semilocal convexity, invexity and
prequasi-invexity, a new kind of generalized convexity called
(strictly/ semistrictly) semilocally prequasi-invex functions is
presented, and some of their basic characterizations are discussed.
Then, several necessary and sufficient conditions for the proposed
generalized convexity are established. Finally, some important properties of the optimal
solutions to the associated generalized convex optimization problems are discussed.