On Some Open Problems in Convex Analysis
Constantin Zălinescu · 1992
In this paper we answer some open problems raised by Rodrigues-Simons [6] and Simons [7]. The answers are given using the celebrated perturbation function method. The starting point for the problems raised in [6] and [7] is to find weaker conditions to have (1) $${(f + gA)^*}({x^*}) = \min \left\{ {{f^*}({x^*} - {A^*}{y^*}) + {g^*}({y^*})|{y^*} \in {Y^*}} \right\}$$ , where X, Y are locally convex spaces, f:X → R̄, g:Y → R̄ are proper convex functions and A:X → Y is a linear operator.