A limited memory adaptive trust-region approach for large-scale unconstrained optimization

Document Type : Research Paper


1 Faculty of Mathematics‎, ‎University of Vienna‎, ‎Oskar-Morge-nstern-Platz 1‎, ‎1090 Vienna‎, ‎Austria.

2 Department of‎ ‎Mathematics‎, ‎Razi University‎, ‎Kermanshah‎, ‎Iran.

3 Department of‎ ‎Mathematics‎, ‎Asadabad Branch‎, ‎Islamic Azad University‎, ‎Asadabad‎, ‎Iran.

4 K.N. Toosi University of Department of‎ ‎Mathematics‎, ‎K‎. ‎N‎. ‎Toosi University of Technology‎, ‎P.O‎. ‎Box 16315-1618‎, ‎Tehran‎, ‎Iran.


This 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.


Main Subjects

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