论文信息 - A Fenchel-Rockafellar type duality theorem for maximization

A Fenchel-Rockafellar type duality theorem for maximization

We prove that sup(f-h)(E) = sup(h*-f*)(E*), where f is a proper lower semi-continuous convex functional on a real locally convex space E, h: E → = [-∞, +∞] is an arbitrary-functional and, f*, h* are their convex conjugates respectively. When h = δG, the indicator of a bounded subset G of E, this yields a formula for sup f(G).

I. Singer | Ivan Singer

[1] I. Singer,et al. Maximization of lower semi-continuous convex functional on bounded subsets of locally convex spaces. II: Quasi-Lagrangian duality theorems , 1980 .

[2] R. Rockafellar. Extension of Fenchel’ duality theorem for convex functions , 1966 .

[3] I. Singer,et al. Some new applications of the Fenchel-Rockafellar duality theorem: Lagrange multiplier theorems and hyperplane theorems for convex optimization and best approximation , 1979 .