Efficient orthogonal factorization for constraint addition and removal in QP based Optimal Power Flows Efficient orthogonal factorization for constraint addition and removal in QP based Optimal Power Flows

A new method for quadratic programming based on orthogonal factorization is presented. The method is suitable for solving the Quadratic Programming problems using the active set approach. The method is based on the Seminormal equations method for solving overdetermined linear equations of the form A′x = B in a least squares sense, with an optional iterative refinement step. Only the R matrix in the QR factorization of A′ is kept. This makes it possible to preserve sparsity for large problems. Updating techniques are used for rotating constraints in and out. Conventional techniques for implementing QP solvers rotate new constraints in and out by adding columns to A′. This paper illustrates how the same effect can be achieved by adding and removing rows to/from A′. The method is based conceptually on the rotation of imaginary rows into R. However, all computations are done using real arithmetic. Examples illustrate the method and applications to Optimum Power Flows and Electricity Spot Pricing are discussed.