On the numerical realization of the exact penalty method for quadratic programming algorithms (Q751516)

The following quadratic nonconvex optimization problem is considered: (P) minimize \(x^ TQx-p^ Tx\) subject to Ax\(\leq b\), where A is an \(m\times n\) matrix and C is symmetric. The aim of the paper is to generalize \textit{K. C. A. Kiwiel}'s algorithm [Wiss. Ber. der TH Leipzig 4, 66-67 (1987)] to obtain a local minimizer of the nonconvex problem (P). An active constraint strategy is used to construct a sequence of equality constrained problems. For these problems a penalty function is defined. Finally, the author discusses how the corresponding unrestricted problems can be solved efficiently.