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Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
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SYSNO ASEP 0532367 Document Type V - Research Report R&D Document Type The record was not marked in the RIV Title Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations Author(s) Vlček, Jan (UIVT-O) SAI, RID, ORCID
Lukšan, Ladislav (UIVT-O) SAI, RIDIssue data Prague: ICS CAS, 2020 Series Technical Report Series number V-1280 Number of pages 21 s. Language eng - English Country CZ - Czech Republic Keywords unconstrained minimization ; variable metric methods ; limited-memory methods ; variationally derived methods ; global convergence ; numerical results Institutional support UIVT-O - RVO:67985807 Annotation Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2021
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