First- and second-order optimality conditions for quadratically constrained quadratic programming problems (Q2139247)

A quadratic programming problem is considered with general quadratic cone constraints and an additional geometric constraint. The necessary and sufficient conditions are established for global optimality for a KKT point or in the presence of the property of strong duality, considering in details the case where the feasible set is defined by two quadratic equality constraints. As a further application, those conditions seem to guarantee the existence of a convex reformulation of a simultaneous diagonalizable quadratic problem.