Optimality condition and quasi-conjugate duality with zero gap in nonconvex optimization (Q2228387)

Nonconvex scalar-minimization and vector-minimization problems are studied. The authors extend the concept of quasi-conjugate function \(f^\ast\) of a functon \(f:\mathbb{R}^n \rightarrow \mathbb{R}\), which was introduced in a paper by \textit{P. T. Thach} [J. Optim. Theory Appl. 188, No. 2, 317--331 (2021; Zbl 1471.90134)] as follows: \[ f^\ast(p) = -\inf \{f(x) \mid p^Tx \geq 1 \}, \forall p \in \mathbb{R}^n. \] Quasi-conjugate duality to a general class of non-convex scalar- and vector- minimization problems is developed. The duality is symmetric and has a zero gap. Optimality conditions in the form of generalized KKT conditions are proved.