TY - GEN TI - Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods T3 - Programs and Algorithms of Numerical Mathematics /19./ AU - Vlček, Jan AB - To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time. The limit update is a block BFGS update. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method. SN - 978-80-85823-69-1 UR - http://hdl.handle.net/11104/0296152 UR - http://www.nusl.cz/ntk/nusl-394990 A2 - Lukšan, Ladislav LA - eng KW - unconstrained minimization KW - the repeated Byrd-Nocedal-Schnabel update KW - the conjugate directions KW - global convergence KW - numerical results KW - limited-memory variable metric methods KW - the Lyapunov matrix equation PY - 2019 PB - Ústav informatiky, Pod vodárenskou věží 2, 182 07 Praha 8, http://www.cs.cas.cz/ ER -