Karush-Kuhn-Tucker type optimality condition for quasiconvex programming in terms of Greenberg-Pierskalla subdifferential
This work deals with the finite-dimensional constrained optimization problem of minimizing an objective function \(f\) on the set \(K=\{x\in \mathbb{R}^{n}:\,g_{i}(x)\leq 0,\,\forall i\in I\}\) where all functions \(f\) and \(g_{i}\), \(i\in I,\) are upper semicontinuous and essentially quasiconvex (that is, they have convex sublevel sets and every local minimum is global). The paper presents necessary and sufficient conditions for the optimality in terms of the Greenberg-Pierskalla subdifferential, which is a subdifferential that had previously used in quasiconvex analysis.
scientific article; zbMATH DE number 7340740
scientific article