In 2013, Buchheim and Wiegele introduced a quadratic optimisation problem, in which the domain of each variable is closed subset reals. This problem includes several other important problems as special cases. We study some convex sets polyhedra associated with derive families strong valid inequalities. also present encouraging computational results, obtained by applying our inequalities to (a) ...

We consider the problem of approximating the global maximum of a quadratic program (QP) subject to bound and (simple) quadratic constraints. Based on several early results, we show that a 4=7-approximate solution can be obtained in polynomial time.

In this paper, we consider the robust linear quadratic (LQ) control problem for a class of uncertain linear systems which are subject to a general type of integral quadratic constraints (IQCs). Both analysis and synthesis problems are considered in this paper. For the analysis problem, we determine if the system satisses a desired linear quadratic performance index for all admissible uncertaint...

We derive closed-form solutions for the linear-quadratic (LQ) optimal control problem subject to integral quadratic constraints. The optimal control is a non-linear function of the current state and the initial state. Furthermore, the optimal control is easily calculated by solving an unconstrained LQ control problem together with an optimal parameter selection problem. Gradient formulae for th...

Quadratically constrained quadratic programs (QQPs) problems play an important modeling role in many diverse problems. These problems are in general NP hard and numerically intractable. Semidefinite programming (SDP) relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation pr...

The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these...

We consider the problem of minimizing an indefinite quadratic function subject to two quadratic inequality constraints. When the problem is defined over the complex plane we show that strong duality holds and obtain necessary and sufficient optimality conditions. We then develop a connection between the image of the real and complex spaces under a quadratic mapping, which together with the resu...

We consider the NP-hard problem of finding a minimum norm vector in n-dimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP) provides an O(m) approximation in the real case, and an O(m) approximation in the complex case. Moreo...