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Jacek Gondzio(J.Gondzioed.ac.uk) Abstract: Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due to problem's inner structure, there are special techniques for efficiently solving linear systems, IPMs enjoy fast convergence and are able to solve large scale optimization problems. It is tempting to try to replace the Newton method by quasiNewton methods. QuasiNewton approaches to IPMs either are built to approximate the Lagrangian function for nonlinear programming problems or provide an inexpensive preconditioner. In this work we study the impact of using quasiNewton methods applied directly to the nonlinear system of equations for general quadratic programming problems. The cost of each iteration can be compared to the cost of computing correctors in a usual interior point iteration. Numerical experiments show that the new approach is able to reduce the overall number of matrix factorizations and is suitable for a matrixfree implementation. Keywords: Broyden Method, QuasiNewton, Interior Point Methods, Matrixfree, Quadratic Programming Problems Category 1: Nonlinear Optimization (Quadratic Programming ) Category 2: Nonlinear Optimization (Nonlinear Systems and LeastSquares ) Citation: Technical Report ERGO 18015, School of Mathematics, June 25, 2018 Download: [PDF] Entry Submitted: 06/26/2018 Modify/Update this entry  
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