Abstract
In the last years a considerable effort was made to treat nonconvex optimization problems. Quite naturally, one direction of research consists in generalizations of the Lagrange concept and numerous papers were published concerning this subject. Besides such investigations, since a couple of years a wide class of nonconvex optimization problems has been considered by DEUMLICH and ELSTER using the concept of generalized conjugate functions. Starting from geometrical properties of the classical FENCHEL’s conjugates, the notion of Φ -conjugate functions was introduced by these authors (cf. /1/, /2/, /4/). The polar theory in projective spaces plays a key role with respect to the geometrical background of Φ -conjugate functions. As in all generalizations of the FENCHEL’s conjugates before, the crucial question is for Φ -conjugates, too, of which way dual problems can be formulated and convenient duality theorems can be proved. It turns out that the theory of Φ -conjugate functions performs a remarkable contribution to the treatment of nonconvex optimization problems. Contributions to the finite dimensional case are given in /2/, /3/, /4/, /15/, /16/.
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