A new version of Farkas' lemma and global convex maximization (Q1312036)

The authors give a nonlinear extension of Farkas' Lemma with a reverse convex inequality and apply the results in order to characterize optimality for the following constrained convex maximization problem without regularity condition: maximize \(f(x)\) subject to \(-g(x)- b\in S\), where \(f\) is continuous and convex and \(\lambda g\) is difference sublinear for each \(\lambda\in S^*\).