On strongly convex and paraconvex dualities. (English) Zbl 0701.49038

Penot, J. P.; Volle, M.

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

Keywords:

strongly convex functions; paraconvex functions; generalized dualities; generalized conjugations; perturbed constrained minimization; duality gap

Citations:

Zbl 0698.00041