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A Generalized Limited-Memory BNS Method Based on the Block BFGS Update
Vlček, Jan ; Lukšan, Ladislav
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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Modifications of the limited-memory BNS method for better satisfaction of previous quasi-Newton conditions
Vlček, Jan ; Lukšan, Ladislav
Several modifications of the limited-memory variable metric BNS method for large scale un- constrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors to improve satisfaction of previous quasi-Newton conditions, utilizing information from previous or subsequent iterations. In case of quadratic objective functions, conjugacy of all stored diffrence vectors and satisfaction of quasi-Newton conditions with these vectors is established. There are many possibilities how to realize this approach and although only two methods were implemented and tested, preliminary numerical results are promising.
Fulltext: content.csg -  PDF
Plný tet: v1127-11 - PDF
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