P , Sequential Quadratic Constrained Quadratic Programming

We follow the popular approach for unconstrained minimization, i.e. we develop a local quadratic model at a current approximate minimizer in conjunction with a trust region. We then minimize this local model in order to nd the next approximate minimizer. Asymptot-ically, nding the local minimizer of the quadratic model is equivalent to applying Newton's method to the stationarity condition. For constrained problems, the local quadratic model corresponds to minimizinga quadratic approximation of the objective subject to quadratic approximations of the constraints (Q 2 P), with an additional trust region. This quadratic model is intractable in general and is usually handled by using linear approximations of the constraints and modifying the Hessian of the objective using the Hessian of the Lagrangean, i.e. a SQP approach. Instead, we solve the Lagrangean relaxation of Q 2 P using semideenite programming. We develop this framework and present an example which illustrates the advantages over the standard SQP approach.