A limited-memory optimization method using the in¯nitely many times repeated BNS update and conjugate directions

Jan Vlcek(vlcelcs.cas.cz)
Ladislav Luksan(luksancs.cas.cz)

Abstract: To improve the performance of the limited-memory variable metric L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed in [1, 2]. But the suitable extra updates need to be selected carefully, since the repeating process can be time consuming. We show that for the limited-memory variable metric BNS method, matrix updating can be e±ciently repeated in¯nitely many times under some conditions, with only a small increase of the number of arithmetic operations. The limit variable metric matrix can be written as a block BFGS update [22], which can be obtained by solving of some low-order Lyapunov matrix equation. The resulting method can be advantageously combined with methods based on vector corrections for conjugacy, see e.g. [21]. Global convergence of the proposed algorithm is established for convex and su±ciently smooth functions. Numerical experiments demonstrate the e±ciency of the new method.

Keywords: Unconstrained minimization, variable metric methods, limited-memory methods, the repeated BFGS update, global convergence, numerical results

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical report No. V 1245, Institute of Computer Science, Czech Academy of Sciences, Prague, March 2018

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Entry Submitted: 05/21/2018
Entry Accepted: 05/21/2018
Entry Last Modified: 05/21/2018

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