Some modifications of the limited-memory variable metric optimization methods

0566981 - ÚI 2023 CZ eng V - Research Report
Vlček, Jan - Lukšan, Ladislav
Some modifications of the limited-memory variable metric optimization methods.
Prague: ICS CAS, 2023. 11 s. Technical Report, V-1290.
Institutional support: RVO:67985807
Keywords : unconstrained minimization * variable metric methods * limited-memory methods * variationally derived methods * arithmetic operations reduction * global convergence

Several modifications of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modified to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new efficient way how to realize the limited-memory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard L-BFGS and BNS methods is given.
Permanent Link: https://hdl.handle.net/11104/0338248