Second-order duality for nonlinear programming (Q1766387)

The authors start with definitions of two notions, namely a sublinear and a second-order \(F\)-pseudoconvex functional. They formulate the problem of minimization of \(f(x)\) under the constraints that \(x\in C_1\), \(g(x)\in C^*_2\), where \(C_1\), \(C_2\) are closed cones, with \(C^*_2\) standing for the polar cone to \(C_2\). Next, they examine four second-order dual models, proving four weak duality results, as well as one strong duality theorem. Finally, they show how to obtain strict converse duality theorems for the four second-order dual models.