Convergence of quasi-Newton matrices generated by the symmetric rank one update
Mathematical Programming: Series A and B
Measures for symmetric rank-one updates
Mathematics of Operations Research
The least prior deviation quasi-Newton update
Mathematical Programming: Series A and B
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
A Modified Rank One Update Which Converges Q-Superlinearly
Computational Optimization and Applications
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Metric-based SR1 updates which are stabilized by a variationalrelaxation of the quasi-Newton relation are examined. Thisinvestigation reveals an interesting and surprising connection to theorigin of quasi-Newton methods as first formulated by Davidon [1]. Anextended version of Davidon‘s original direct prediction SR1 updateis shown to be self-complementary and to possess a finite terminationproperty on quadratics, and limited-memory versions of the update areshown to be globally convergent. Variants of this update are testednumerically and compared to several other metric-based SR1 variantsand the BFGS update. Finally, metric-based stabilizations of the SR1update are critiqued in general, and a promising new model-basedstrategy recently developed is briefly described.