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Article

Vlček, Jan ; Lukšan, Ladislav
A generalized limited-memory BNS method based on the block BFGS update. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Janov nad Nisou, June 19-24, 2016. Institute of Mathematics CAS, Prague, 2017. pp. 164-171
MSC: 65K10 | DOI: 10.21136/panm.2016.19
Keywords:
unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results
Summary:
A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in some sense for quadratic objective functions, but it does not guarantee that the direction vectors are descent for general functions. To overcome this difficulty and utilize the advantageous properties of the block BFGS update, a block version of the limited-memory BNS method for large scale unconstrained optimization is proposed. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency.
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