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National Repository of Grey Literature

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	Modifications of the limited-memory BFGS method based on the idea of conjugate directions Vlček, Jan ; Lukšan, Ladislav Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly. Detailed record
	Efficient tridiagonal preconditioner for the matrix-free truncated Newton method Lukšan, Ladislav ; Vlček, Jan Fulltext: content.csg - PDF Plný tet: v1177-13 - PDF Detailed record
	Band preconditioners for the matrix-free truncated Newton method Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan Fulltext: content.csg - PDF Plný tet: v1079-10 - PDF Detailed record
	Recursive formulation of limited memory variable metric methods Lukšan, Ladislav ; Vlček, Jan Fulltext: content.csg - PDF Plný tet: v1059-10 - PDF Detailed record
	Metody s proměnnou metrikou pro optimalizaci speciálních rozsáhlých nehladkých funkcí Lukšan, Ladislav ; Vlček, Jan In this contribution, we propose a new partitioned variable metric method for minimizing nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new method. Detailed record

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