HIDDEN CONVEXITY IN SOME NONCONVEX QUADRATICALLY CONSTRAINED QUADRATIC-PROGRAMMING

We consider the problem of minimizing an indefinite quadratic objectiv e function subject to two-sided indefinite quadratic constraints. Unde r a suitable simultaneous diagonalization assumption (which trivially holds for trust region type problems), we prove that the original prob lem is equivalent to a convex minimization problem with simple linear constraints. We then consider a special problem of minimizing a concav e quadratic function subject to finitely many convex quadratic constra ints, which is also shown to be equivalent to a minimax convex problem . Tn both cases we derive the explicit nonlinear transformations which allow for recovering the optimal solution of the nonconvex problems v ia their equivalent convex counterparts. Special cases and application s are also discussed. We outline interior-point polynomial-time algori thms for the solution of the equivalent convex programs.