Semicontinuity and quasiconvex functions. (English) Zbl 0892.90145

Summary: Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is \(r\)-convex in the sense given by Avriel.


90C25 Convex programming
26B25 Convexity of real functions of several variables, generalizations
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