Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801A limited memory adaptive trust-region approach for large-scale unconstrained optimization819837835ENM.AhookhoshFaculty of Mathematics, University of Vienna, Oskar-Morge-nstern-Platz 1, 1090 Vienna, Austria.K.AminiDepartment of
Mathematics, Razi University, Kermanshah, Iran.M.KimiaeiDepartment of
Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.M. R.PeyghamiK.N. Toosi University of Department of
Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.Journal Article20131115This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newton formulas helps to handle large-scale problems. Theoretical analysis indicates that the new approach preserves the global convergence to a first-order stationary point under classical assumptions. Moreover, the superlinear and the quadratic convergence rates are also established under suitable conditions. Preliminary numerical experiments show the effectiveness of the proposed approach for solving large-scale unconstrained optimization problems.http://bims.iranjournals.ir/article_835_05d125fc7788d3d72bb2e454b7c9ae39.pdf