We consider convex relaxations for the problem of minimizing a (possibly nonconvex) quadratic objective subject to linear and (possibly nonconvex) quadratic constraints. Let F denote the feasible region for the linear constraints. We first show that replacing the quadratic objective and constraint functions with their convex lower envelopes on F is dominated by an alternative methodology based ...

In this paper, stability conditions for distributed control problems are derived under general integral quadratic constraints to achieve quadratic performance. These results take the form of coupled LMIs, and the multipliers are specified by the underlying integral quadratic constraints to model interconnections between the subsystems. It is further shown that these stability results can be exp...

Large convex quadratic programs, where constraints are of box type only, can be solved quite eeciently 1], 2], 12], 13], 16]. In this paper an exact quadratic augmented Lagrangian with bound constraints is constructed which allows one to use these methods for general constrained convex quadratic programming. This is in contrast to well known exact diierentiable penalty functions for this type o...

An innnite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered. We generalize the interior-point techniques of Nesterov-Nemirovsky to this innnite-dimensional situation. The obtained complexity estimates are similar to nite-dimensional ones. We apply our results to the linear-quadratic control problem with quadratic cons...

A linearization technique is developed for multi-objective multi-quadratic 0-1 programming problems with linear and quadratic constraints to reduce it to multi-objective linear mixed 0-1 programming problems. The method proposed in this paper needs only O (kn) additional continuous variables where k is the number of quadratic constraints and n is the number of initial 0-1 variables.

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to...