Duality in generalized homogeneous programming
The author studies the generalized homogeneous programming problem \[ (HP)\quad Find\quad M=\inf \{f(x):x\in S\}\quad with\quad S=\{x\in P:g(w)\leq \Psi (x,w)\quad for\quad all\quad w\in Q^ 0\} \] and its dual problem \[ (DHP)\quad Find\quad M^*=\sup \{g(w):w\in S^*\}\quad with\quad S^*=\{w\in Q^ 0:f(x)\geq \Psi (x,w)\quad for\quad all\quad x\in P\} \] where P, \(Q^ 0\) are closed convex cones, and f, -g, \(\Psi\) (x,.) (for all x), and -\(\Psi\) (.,w) (for all w) are lower semi- continuous and sublinear. Under certain conditions on the data, weak and strong duality theorems are shown, which partly improve or generalize known results by \textit{M. Schechter} [J. Optimization Theory Appl. 23, 389-400 (1977; Zbl 0387.90089)].
scientific article; zbMATH DE number 3886628