Scaled constraint qualifications and necessary optimality conditions for nonsmooth mathematical programs with second-order cone complementarity constraints
The following minimization problem with second-order cone complementarity constraints is considered: \[ f(z) \rightarrow \min \text{ subject to } G_i(z) \in K_{m_i},~ H_i(z) \subset K_{m_i},~ (G_i(z),H_i(z)) = 0,~ i = 1,\dots, J, \] where \(f: \mathbb{R}^n \rightarrow \mathbb{R},~ G_i: \mathbb{R}^n \rightarrow \mathbb{R}^{m_i},~ i = 1,\dots J\) and \(K_{m_i}\) denotes for all \(i\) the \(m_i\)-dimensional second-order cone. Applications of the minimization problem and their modifications are outlined. It is shown that usually used constraint qualifications as Mangasarian-Fromowitz constraint qualifications cannot be used for this problem. The authors propose new constraint qualifications and study properties of the corresponding new stationary concepts.
mathematical program with second-order cone complementarity constraints
scientific article; zbMATH DE number 7490100
scientific article