Duality for nondifferentiable nonlinear programming problems: A feasible direction approach (Q1184766)

The authors consider the optimization problem (P): max \(g(x)\) over the set \(X=\{x\in\mathbb{R}^ n\mid f_ j(x)\) \(\geq 0\), \(j=1,\dots,m\}\), where the functions \(g\), \(f_ 1,\dots,f_ m\) are proper real functions on \(\mathbb{R}^ n\) but not necessarily differentiable. It is shown that a generalized dual of (P) defined in terms of Dini derivatives can be a useful tool of solving (P) specially in the case when \(g\) is pseudoconcave.