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On strongly convex and paraconvex dualities. (English) Zbl 0701.49038
Generalized convexity and fractional programming with economic applications, Proc. Workshop, Pisa/Italy 1988, Lect. Notes Econ. Math. Syst. 345, 198-218 (1990).
Summary: [For the entire collection see Zbl 0698.00041.]
The notions of strongly convex functions and paraconvex functions are examined under the light of generalized dualities; exact generalized conjugations for strongly convex functions and paraconvex functions are established and a condition ensuring the paraconvexity of the value function of a perturbed constrained minimization problem is given. Furthermore a dual problem with respect to generalized conjugation is introduced and a condition ensuring the absence of a duality gap is given.

MSC:
49N15 Duality theory (optimization)
90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations
49J52 Nonsmooth analysis