Dai YH (2002) Convergence properties of the BFGS algoritm. SIAM J Optim 13:693-701Dai, YH: Convergence properties of the BFGS algoritm. SIAM J. Optim. 13(3), 693-701 (2002)Y.-H. Dai. Convergence properties of th
This work is devoted to convergence properties of the Broyden-like method for systems of equations in which some of the equations are linear. Among others, it provides the first answer to the decades-old question whether the Broyden-like matrices converge under the standard assumptions for q-supe...
methodsusingtheSR1,PSB,andBFGSupdatesareeffectivemethodsforsolving unconstrainedoptimizationproblems.Inaddition,theanalysesinPowell[1975] andByrd,Khalfan,andSchnabel[1993]demonstratestrongconvergenceproperties forsometrust-regionquasi-Newtonmethods.Acomputationaldisadvantageofthe methodsanalyzedinthesepapers,forwhichthe...
2.The parametric iterative methods of quadratic convergence without the derivative for solving nonlinear equations are discussed in this paper.虽然它一般至少是二阶收敛的,但它需要调用导数值,这使其应用受到限制。 3.An attractive property of the structured BFGS method is its local superlinear/quadratic co...
[ 28 ]. while the per-iteration cost of stochastic newton methods based on sketch-and-project is generally lower than that of the aforementioned newton sketch methods, their convergence rates are more sensitive to the spectral properties of the hessian. the precise characterizations of the ...
During the struc- tural optimization, a limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm was applied and the total energy in PBE exchange-correlation functional was used in calculating the formation energy per atom. The convergence criteria was set to 0.01 eV A−1 of ...
A new smoothing function and its properties We construct the following smoothing function:φ(μ,t)=0,ift⩾μ,112μ(μ-t)3,if|t|<μ,12t2+16μ2,ift⩽-μ,where μ ⩾ 0 is a smoothing parameter. The new smoothing function possesses a few nice properties. Especially, it is twice co...
6, 279 - 284 Convergence of an Adaptive Newton Algorithm Sanjay Kumar Khattri Stord/Haugesund University College Norway sanjay.khattri@hsh.no Abstract The Newton - Krylov iteration is the most prominent iterative method for solving non-linear system of equations (F(x)). Roughly speaking, the ...
ConvergenceSuperlinearconvergence.1.IntroductionAssumethatwearefindingtheminimizerofthefollowingunconstrainedoptimizationproblemminf(x),(1.1)acReandassumethecurrentpointisxk'TOcalculatexk+1fromxkbyalinesearchmethod,thefollowingiterationXk+1~Xk+Akpk,k~1,2,'''(1.2)isapplied.IntheBFGSal...计算数学(英文版)...
Presents a study which showed that the modified BFGS algorithm is globally and superlinearly convergent based on the Armijo-Goldstein line searches. Main results; Theorems; Proofs.Nai-yang DengZheng-feng LiJournal of Computational MathematicsNai-yang Deng and Zheng-feng Li, Convergence properties of ...