Solving conic quadratically constrained quadratic programming problems (Q2928413)

The paper is concerned with the conic quadratically constrained quadratic programming problem (CQCQP) and extends results by \textit{C. Lu} et al. [SIAM J. Optim. 21, No. 4, 1475--1490 (2011; Zbl 1242.49044)] for the quadratically constrained quadratic programming problem (QCQP). In particular, KKT conditions for CQCQP and related linear conic reformulations of this problem using the cone of nonnegative quadratic functions are introduced. Moreover, an extended copositiveness condition is proved, which is an extended global optimality condition similar to that by \textit{C. Lu} et al. for QCQP, and an extended global optimality condition is given, which is based on an extended maximal property of the optimal Lagrangian multipliers. This allows the set-up of a computational scheme for the solution of CQCQP under additional assumptions. An example demonstrates the performance of the proposed algorithm.