Berahas, A. S.; Jahani, M.; Richtárik, P.; Takáč, M. Quasi-Newton methods for machine learning: forget the past, just sample. (English) Zbl 07634895 Optim. Methods Softw. 37, No. 5, 1668-1704 (2022). MSC: 90Cxx 65Kxx PDF BibTeX XML Cite \textit{A. S. Berahas} et al., Optim. Methods Softw. 37, No. 5, 1668--1704 (2022; Zbl 07634895) Full Text: DOI arXiv OpenURL
Yuan, Gonglin; Wang, Zhan; Li, Pengyuan Global convergence of a modified Broyden family method for nonconvex functions. (English) Zbl 07590624 J. Ind. Manag. Optim. 18, No. 6, 4393-4407 (2022). MSC: 90C53 PDF BibTeX XML Cite \textit{G. Yuan} et al., J. Ind. Manag. Optim. 18, No. 6, 4393--4407 (2022; Zbl 07590624) Full Text: DOI OpenURL
Yuan, Gonglin; Wang, Zhan; Li, Pengyuan Global convergence of a nonmonotone Broyden family method for nonconvex unconstrained minimization. (English) Zbl 1498.90228 Comput. Appl. Math. 41, No. 6, Paper No. 272, 15 p. (2022). MSC: 90C30 PDF BibTeX XML Cite \textit{G. Yuan} et al., Comput. Appl. Math. 41, No. 6, Paper No. 272, 15 p. (2022; Zbl 1498.90228) Full Text: DOI OpenURL
Yuan, Gonglin; Li, Pengyuan; Lu, Junyu The global convergence of the BFGS method with a modified WWP line search for nonconvex functions. (English) Zbl 1496.65079 Numer. Algorithms 91, No. 1, 353-365 (2022). MSC: 65K05 90C26 90C53 PDF BibTeX XML Cite \textit{G. Yuan} et al., Numer. Algorithms 91, No. 1, 353--365 (2022; Zbl 1496.65079) Full Text: DOI OpenURL
Prudente, L. F.; Souza, D. R. A quasi-Newton method with Wolfe line searches for multiobjective optimization. (English) Zbl 1492.90163 J. Optim. Theory Appl. 194, No. 3, 1107-1140 (2022). MSC: 90C29 90C53 90C30 65K05 PDF BibTeX XML Cite \textit{L. F. Prudente} and \textit{D. R. Souza}, J. Optim. Theory Appl. 194, No. 3, 1107--1140 (2022; Zbl 1492.90163) Full Text: DOI OpenURL
Berahas, Albert S.; Curtis, Frank E.; Zhou, Baoyu Limited-memory BFGS with displacement aggregation. (English) Zbl 1492.65161 Math. Program. 194, No. 1-2 (A), 121-157 (2022). MSC: 65K05 65K10 90C30 90C53 49M37 PDF BibTeX XML Cite \textit{A. S. Berahas} et al., Math. Program. 194, No. 1--2 (A), 121--157 (2022; Zbl 1492.65161) Full Text: DOI arXiv OpenURL
Tankaria, Hardik; Sugimoto, Shinji; Yamashita, Nobuo A regularized limited memory BFGS method for large-scale unconstrained optimization and its efficient implementations. (English) Zbl 1490.90282 Comput. Optim. Appl. 82, No. 1, 61-88 (2022). MSC: 90C30 90C06 PDF BibTeX XML Cite \textit{H. Tankaria} et al., Comput. Optim. Appl. 82, No. 1, 61--88 (2022; Zbl 1490.90282) Full Text: DOI arXiv OpenURL
El Yazidi, Youness; Ellabib, Abdellatif Augmented Lagrangian approach for a bilateral free boundary problem. (English) Zbl 1490.49029 J. Appl. Math. Comput. 67, No. 1-2, 69-88 (2021). MSC: 49Q10 65M60 49M15 PDF BibTeX XML Cite \textit{Y. El Yazidi} and \textit{A. Ellabib}, J. Appl. Math. Comput. 67, No. 1--2, 69--88 (2021; Zbl 1490.49029) Full Text: DOI OpenURL
Dehghani, R.; Bidabadi, N.; Hosseini, M. M. Using nonlinear functions to approximate a new quasi-Newton method for unconstrained optimization problems. (English) Zbl 1465.65050 Numer. Algorithms 87, No. 2, 755-777 (2021). MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{R. Dehghani} et al., Numer. Algorithms 87, No. 2, 755--777 (2021; Zbl 1465.65050) Full Text: DOI OpenURL
Leong, Wah June; Enshaei, Sharareh; Kek, Sie Long Diagonal quasi-Newton methods via least change updating principle with weighted Frobenius norm. (English) Zbl 1464.90099 Numer. Algorithms 86, No. 3, 1225-1241 (2021). MSC: 90C30 90C53 65K10 PDF BibTeX XML Cite \textit{W. J. Leong} et al., Numer. Algorithms 86, No. 3, 1225--1241 (2021; Zbl 1464.90099) Full Text: DOI OpenURL
Li, Pengyuan; Wang, Zhan; Luo, Dan; Pham, Hongtruong Global convergence of a modified two-parameter scaled BFGS method with Yuan-Wei-Lu line search for unconstrained optimization. (English) Zbl 1459.90167 Math. Probl. Eng. 2020, Article ID 9280495, 15 p. (2020). MSC: 90C26 90C53 90C30 65K05 PDF BibTeX XML Cite \textit{P. Li} et al., Math. Probl. Eng. 2020, Article ID 9280495, 15 p. (2020; Zbl 1459.90167) Full Text: DOI OpenURL
Yuan, Gonglin; Wang, Xiaoliang; Sheng, Zhou The projection technique for two open problems of unconstrained optimization problems. (English) Zbl 1450.90037 J. Optim. Theory Appl. 186, No. 2, 590-619 (2020). MSC: 90C26 90C53 PDF BibTeX XML Cite \textit{G. Yuan} et al., J. Optim. Theory Appl. 186, No. 2, 590--619 (2020; Zbl 1450.90037) Full Text: DOI OpenURL
Bojari, S.; Eslahchi, M. R. Global convergence of a family of modified BFGS methods under a modified weak-Wolfe-Powell line search for nonconvex functions. (English) Zbl 1445.90085 4OR 18, No. 2, 219-244 (2020). MSC: 90C26 90C53 PDF BibTeX XML Cite \textit{S. Bojari} and \textit{M. R. Eslahchi}, 4OR 18, No. 2, 219--244 (2020; Zbl 1445.90085) Full Text: DOI OpenURL
An, Congpei; Xiao, Yuchen Numerical construction of spherical \(t\)-designs by Barzilai-Borwein method. (English) Zbl 1434.65020 Appl. Numer. Math. 150, 295-302 (2020). MSC: 65D18 65D32 05B30 65K05 PDF BibTeX XML Cite \textit{C. An} and \textit{Y. Xiao}, Appl. Numer. Math. 150, 295--302 (2020; Zbl 1434.65020) Full Text: DOI arXiv OpenURL
Asl, Azam; Overton, Michael L. Analysis of the gradient method with an Armijo-Wolfe line search on a class of non-smooth convex functions. (English) Zbl 1437.90124 Optim. Methods Softw. 35, No. 2, 223-242 (2020). MSC: 90C25 65K05 PDF BibTeX XML Cite \textit{A. Asl} and \textit{M. L. Overton}, Optim. Methods Softw. 35, No. 2, 223--242 (2020; Zbl 1437.90124) Full Text: DOI arXiv OpenURL
Xie, Yuchen; Byrd, Richard H.; Nocedal, Jorge Analysis of the BFGS method with errors. (English) Zbl 1435.90149 SIAM J. Optim. 30, No. 1, 182-209 (2020). MSC: 90C56 90C53 90C30 PDF BibTeX XML Cite \textit{Y. Xie} et al., SIAM J. Optim. 30, No. 1, 182--209 (2020; Zbl 1435.90149) Full Text: DOI arXiv OpenURL
Berahas, Albert S.; Takáč, Martin A robust multi-batch L-BFGS method for machine learning. (English) Zbl 1430.90523 Optim. Methods Softw. 35, No. 1, 191-219 (2020). MSC: 90C30 90C06 90C53 65K05 68T09 PDF BibTeX XML Cite \textit{A. S. Berahas} and \textit{M. Takáč}, Optim. Methods Softw. 35, No. 1, 191--219 (2020; Zbl 1430.90523) Full Text: DOI arXiv OpenURL
Dehghani, Razieh; Hosseini, Mohmadmehdi Using a modied secant equation for unconstrained optimization. (English) Zbl 1454.90113 J. Math. Ext. 13, No. 1, 103-116 (2019). MSC: 90C53 49M37 65K05 PDF BibTeX XML Cite \textit{R. Dehghani} and \textit{M. Hosseini}, J. Math. Ext. 13, No. 1, 103--116 (2019; Zbl 1454.90113) Full Text: Link OpenURL
Ochs, Peter; Pock, Thomas Adaptive FISTA for nonconvex optimization. (English) Zbl 1461.65180 SIAM J. Optim. 29, No. 4, 2482-2503 (2019). MSC: 65K05 90C25 90C26 90C53 PDF BibTeX XML Cite \textit{P. Ochs} and \textit{T. Pock}, SIAM J. Optim. 29, No. 4, 2482--2503 (2019; Zbl 1461.65180) Full Text: DOI arXiv OpenURL
Cipolla, Stefano; Di Fiore, Carmine; Zellini, Paolo Low complexity matrix projections preserving actions on vectors. (English) Zbl 1415.65069 Calcolo 56, No. 2, Paper No. 8, 21 p. (2019). MSC: 65F08 90C06 90C53 15B10 PDF BibTeX XML Cite \textit{S. Cipolla} et al., Calcolo 56, No. 2, Paper No. 8, 21 p. (2019; Zbl 1415.65069) Full Text: DOI OpenURL
Livieris, Ioannis E.; Tampakas, Vassilis; Pintelas, Panagiotis A descent hybrid conjugate gradient method based on the memoryless BFGS update. (English) Zbl 06986853 Numer. Algorithms 79, No. 4, 1169-1185 (2018). MSC: 65-XX PDF BibTeX XML Cite \textit{I. E. Livieris} et al., Numer. Algorithms 79, No. 4, 1169--1185 (2018; Zbl 06986853) Full Text: DOI OpenURL
Guo, Jiayi; Lewis, A. S. Nonsmooth variants of Powell’s BFGS convergence theorem. (English) Zbl 1397.90358 SIAM J. Optim. 28, No. 2, 1301-1311 (2018). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{J. Guo} and \textit{A. S. Lewis}, SIAM J. Optim. 28, No. 2, 1301--1311 (2018; Zbl 1397.90358) Full Text: DOI OpenURL
Gao, Wenbo; Goldfarb, Donald Block BFGS methods. (English) Zbl 1397.90402 SIAM J. Optim. 28, No. 2, 1205-1231 (2018). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 90C53 90C26 PDF BibTeX XML Cite \textit{W. Gao} and \textit{D. Goldfarb}, SIAM J. Optim. 28, No. 2, 1205--1231 (2018; Zbl 1397.90402) Full Text: DOI arXiv OpenURL
Yuan, Gonglin; Sheng, Zhou; Wang, Bopeng; Hu, Wujie; Li, Chunnian The global convergence of a modified BFGS method for nonconvex functions. (English) Zbl 1370.90203 J. Comput. Appl. Math. 327, 274-294 (2018). MSC: 90C26 PDF BibTeX XML Cite \textit{G. Yuan} et al., J. Comput. Appl. Math. 327, 274--294 (2018; Zbl 1370.90203) Full Text: DOI OpenURL
Yuan, Gonglin; Wei, Zengxin; Lu, Xiwen Global convergence of BFGS and PRP methods under a modified weak Wolfe-Powell line search. (English) Zbl 1446.65031 Appl. Math. Modelling 47, 811-825 (2017). MSC: 65K05 90C26 PDF BibTeX XML Cite \textit{G. Yuan} et al., Appl. Math. Modelling 47, 811--825 (2017; Zbl 1446.65031) Full Text: DOI OpenURL
Zabinyako, Gerard Idelfonovich Applications of quasi-Newton algorithms for solving large scale problems. (Russian. English summary) Zbl 06870925 Vychisl. Tekhnol. 22, No. 5, 47-57 (2017). MSC: 65Kxx PDF BibTeX XML Cite \textit{G. I. Zabinyako}, Vychisl. Tekhnol. 22, No. 5, 47--57 (2017; Zbl 06870925) Full Text: Link OpenURL
Stella, Lorenzo; Themelis, Andreas; Patrinos, Panagiotis Forward-backward quasi-Newton methods for nonsmooth optimization problems. (English) Zbl 1401.90226 Comput. Optim. Appl. 67, No. 3, 443-487 (2017). MSC: 90C30 PDF BibTeX XML Cite \textit{L. Stella} et al., Comput. Optim. Appl. 67, No. 3, 443--487 (2017; Zbl 1401.90226) Full Text: DOI arXiv OpenURL
Leong, Wah June A class of diagonal quasi-Newton methods for large-scale convex minimization. (English) Zbl 1357.65075 Bull. Malays. Math. Sci. Soc. (2) 39, No. 4, 1659-1672 (2016). Reviewer: Hang Lau (Montréal) MSC: 65K05 90C25 90C53 90C06 PDF BibTeX XML Cite \textit{W. J. Leong}, Bull. Malays. Math. Sci. Soc. (2) 39, No. 4, 1659--1672 (2016; Zbl 1357.65075) Full Text: DOI Link OpenURL
Byrd, R. H.; Hansen, S. L.; Nocedal, Jorge; Singer, Y. A stochastic quasi-Newton method for large-scale optimization. (English) Zbl 1382.65166 SIAM J. Optim. 26, No. 2, 1008-1031 (2016). MSC: 65K05 90C06 90C30 90C53 90C55 PDF BibTeX XML Cite \textit{R. H. Byrd} et al., SIAM J. Optim. 26, No. 2, 1008--1031 (2016; Zbl 1382.65166) Full Text: DOI arXiv OpenURL
Liu, Li A new BFGS algorithm using the decomposition matrix of the correction matrix to obtain the search directions. (English) Zbl 1326.93047 J. Control Sci. Eng. 2015, Article ID 674617, 8 p. (2015). MSC: 93B40 90C53 PDF BibTeX XML Cite \textit{L. Liu}, J. Control Sci. Eng. 2015, Article ID 674617, 8 p. (2015; Zbl 1326.93047) Full Text: DOI OpenURL
Liu, Hao; Shao, Jianfeng; Wang, Haijun; Chang, Baoxian An adaptive sizing BFGS method for unconstrained optimization. (English) Zbl 1319.65049 Calcolo 52, No. 2, 233-244 (2015). MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{H. Liu} et al., Calcolo 52, No. 2, 233--244 (2015; Zbl 1319.65049) Full Text: DOI OpenURL
Lewis, A. S.; Zhang, Shanshan Nonsmoothness and a variable metric method. (English) Zbl 1322.90095 J. Optim. Theory Appl. 165, No. 1, 151-171 (2015). MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{A. S. Lewis} and \textit{S. Zhang}, J. Optim. Theory Appl. 165, No. 1, 151--171 (2015; Zbl 1322.90095) Full Text: DOI OpenURL
Petrović, Milena J.; Stanimirović, Predrag S. Accelerated double direction method for solving unconstrained optimization problems. (English) Zbl 1407.90262 Math. Probl. Eng. 2014, Article ID 965104, 8 p. (2014). MSC: 90C26 90C53 65K05 PDF BibTeX XML Cite \textit{M. J. Petrović} and \textit{P. S. Stanimirović}, Math. Probl. Eng. 2014, Article ID 965104, 8 p. (2014; Zbl 1407.90262) Full Text: DOI OpenURL
Xiao, Yun-hai; Li, Ting-feng; Wei, Zeng-xin Global convergence of a modified limited memory BFGS method for non-convex minimization. (English) Zbl 1303.65048 Acta Math. Appl. Sin., Engl. Ser. 29, No. 3, 555-566 (2013). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C30 90C06 PDF BibTeX XML Cite \textit{Y.-h. Xiao} et al., Acta Math. Appl. Sin., Engl. Ser. 29, No. 3, 555--566 (2013; Zbl 1303.65048) Full Text: DOI OpenURL
Lewis, Adrian S.; Overton, Michael L. Nonsmooth optimization via quasi-Newton methods. (English) Zbl 1280.90118 Math. Program. 141, No. 1-2 (A), 135-163 (2013). MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{A. S. Lewis} and \textit{M. L. Overton}, Math. Program. 141, No. 1--2 (A), 135--163 (2013; Zbl 1280.90118) Full Text: DOI OpenURL
Al-Baali, Mehiddin; Khalfan, Humaid A combined class of self-scaling and modified quasi-Newton methods. (English) Zbl 1250.90112 Comput. Optim. Appl. 52, No. 2, 393-408 (2012). MSC: 90C53 90C30 PDF BibTeX XML Cite \textit{M. Al-Baali} and \textit{H. Khalfan}, Comput. Optim. Appl. 52, No. 2, 393--408 (2012; Zbl 1250.90112) Full Text: DOI OpenURL
Fanelli, Stefano Gradient-type methods: a unified perspective in computer science and numerical analysis. (English) Zbl 1238.65054 ISRN Appl. Math. 2011, Article ID 715748, 22 p. (2011). MSC: 65K05 PDF BibTeX XML Cite \textit{S. Fanelli}, ISRN Appl. Math. 2011, Article ID 715748, 22 p. (2011; Zbl 1238.65054) Full Text: DOI OpenURL
Babaie-Kafaki, Saman A modified BFGS algorithm based on a hybrid secant equation. (English) Zbl 1401.90268 Sci. China, Math. 54, No. 9, 2019-2036 (2011). MSC: 90C53 49M37 65K05 PDF BibTeX XML Cite \textit{S. Babaie-Kafaki}, Sci. China, Math. 54, No. 9, 2019--2036 (2011; Zbl 1401.90268) Full Text: DOI OpenURL
Fanelli, S. A new algorithm for box-constrained global optimization. (English) Zbl 1221.90073 J. Optim. Theory Appl. 149, No. 1, 175-196 (2011). MSC: 90C26 90C52 PDF BibTeX XML Cite \textit{S. Fanelli}, J. Optim. Theory Appl. 149, No. 1, 175--196 (2011; Zbl 1221.90073) Full Text: DOI OpenURL
Biglari, Fahimeh; Hassan, Malik Abu; Leong, Wah June New quasi-Newton methods via higher order tensor models. (English) Zbl 1211.65068 J. Comput. Appl. Math. 235, No. 8, 2412-2422 (2011). Reviewer: Hang Lau (Montréal) MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{F. Biglari} et al., J. Comput. Appl. Math. 235, No. 8, 2412--2422 (2011; Zbl 1211.65068) Full Text: DOI OpenURL
Liu, Liying; Wei, Zengxin; Wu, Xiaoping The convergence of a new modified BFGS method without line searches for unconstrained optimization or complexity systems. (English) Zbl 1209.90321 J. Syst. Sci. Complex. 23, No. 4, 861-872 (2010). MSC: 90C30 PDF BibTeX XML Cite \textit{L. Liu} et al., J. Syst. Sci. Complex. 23, No. 4, 861--872 (2010; Zbl 1209.90321) Full Text: DOI OpenURL
Yuan, Gonglin; Wei, Zengxin Convergence analysis of a modified BFGS method on convex minimizations. (English) Zbl 1228.90077 Comput. Optim. Appl. 47, No. 2, 237-255 (2010). MSC: 90C25 PDF BibTeX XML Cite \textit{G. Yuan} and \textit{Z. Wei}, Comput. Optim. Appl. 47, No. 2, 237--255 (2010; Zbl 1228.90077) Full Text: DOI OpenURL
Stanimirović, Predrag S.; Miladinović, Marko B. Accelerated gradient descent methods with line search. (English) Zbl 1198.65104 Numer. Algorithms 54, No. 4, 503-520 (2010). Reviewer: Karel Zimmermann (Praha) MSC: 65K05 PDF BibTeX XML Cite \textit{P. S. Stanimirović} and \textit{M. B. Miladinović}, Numer. Algorithms 54, No. 4, 503--520 (2010; Zbl 1198.65104) Full Text: DOI OpenURL
Xie, Dexuan; Ni, Qin An incomplete Hessian Newton minimization method and its application in a chemical database problem. (English) Zbl 1181.90195 Comput. Optim. Appl. 44, No. 3, 467-485 (2009). MSC: 90C06 90C30 90C53 PDF BibTeX XML Cite \textit{D. Xie} and \textit{Q. Ni}, Comput. Optim. Appl. 44, No. 3, 467--485 (2009; Zbl 1181.90195) Full Text: DOI Link OpenURL
Andrei, Neculai Acceleration of conjugate gradient algorithms for unconstrained optimization. (English) Zbl 1172.65027 Appl. Math. Comput. 213, No. 2, 361-369 (2009). Reviewer: Vasilis Dimitriou (Chania) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{N. Andrei}, Appl. Math. Comput. 213, No. 2, 361--369 (2009; Zbl 1172.65027) Full Text: DOI OpenURL
Xiao, Yunhai; Sun, Huijuan; Wang, Zhiguo A globally convergent BFGS method with nonmonotone line search for non-convex minimization. (English) Zbl 1169.65058 J. Comput. Appl. Math. 230, No. 1, 95-106 (2009). Reviewer: Hang Lau (Montréal) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{Y. Xiao} et al., J. Comput. Appl. Math. 230, No. 1, 95--106 (2009; Zbl 1169.65058) Full Text: DOI OpenURL
Li, Donghui; Qi, Liqun; Roshchina, Vera A new class of quasi-Newton updating formulas. (English) Zbl 1211.90293 Optim. Methods Softw. 23, No. 2, 237-249 (2008). MSC: 90C53 65K10 PDF BibTeX XML Cite \textit{D. Li} et al., Optim. Methods Softw. 23, No. 2, 237--249 (2008; Zbl 1211.90293) Full Text: DOI OpenURL
Guo, Qiang; Liu, Jian-Guo; Wang, Dan-Hong A modified BFGS method and its superlinear convergence in nonconvex minimization with general line search rule. (English) Zbl 1170.65048 J. Appl. Math. Comput. 28, No. 1-2, 435-446 (2008). Reviewer: Maciek Korzec (Berlin) MSC: 65K05 90C26 PDF BibTeX XML Cite \textit{Q. Guo} et al., J. Appl. Math. Comput. 28, No. 1--2, 435--446 (2008; Zbl 1170.65048) Full Text: DOI OpenURL
Liu, Liying; Yao, Shengwei; Wei, Zengxin The global and superlinear convergence of a new nonmonotone MBFGS algorithm on convex objective functions. (English) Zbl 1152.65068 J. Comput. Appl. Math. 220, No. 1-2, 422-438 (2008). Reviewer: Maciek Korzec (Berlin) MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{L. Liu} et al., J. Comput. Appl. Math. 220, No. 1--2, 422--438 (2008; Zbl 1152.65068) Full Text: DOI OpenURL
Yu, Zhensheng; Pu, Dingguo A new nonmonotone line search technique for unconstrained optimization. (English) Zbl 1149.65045 J. Comput. Appl. Math. 219, No. 1, 134-144 (2008). Reviewer: Stefan Mititelu (Bucureşti) MSC: 65K05 90C53 90C30 PDF BibTeX XML Cite \textit{Z. Yu} and \textit{D. Pu}, J. Comput. Appl. Math. 219, No. 1, 134--144 (2008; Zbl 1149.65045) Full Text: DOI OpenURL
Yuan, Gong Lin; Wei, Zeng Xin The superlinear convergence analysis of a nonmonotone BFGS algorithm on convex objective functions. (English) Zbl 1152.65072 Acta Math. Sin., Engl. Ser. 24, No. 1, 35-42 (2008). Reviewer: Nicolae Popovici (Cluj-Napoca) MSC: 65K05 90C25 PDF BibTeX XML Cite \textit{G. L. Yuan} and \textit{Z. X. Wei}, Acta Math. Sin., Engl. Ser. 24, No. 1, 35--42 (2008; Zbl 1152.65072) Full Text: DOI OpenURL
Di Fiore, Carmine; Fanelli, Stefano; Zellini, Paolo Low complexity secant quasi-Newton minimization algorithms for nonconvex functions. (English) Zbl 1139.65047 J. Comput. Appl. Math. 210, No. 1-2, 167-174 (2007). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 65K05 90C53 90C26 PDF BibTeX XML Cite \textit{C. Di Fiore} et al., J. Comput. Appl. Math. 210, No. 1--2, 167--174 (2007; Zbl 1139.65047) Full Text: DOI OpenURL
Guo, Qiang; Liu, Jianguo Global convergence of a modified BFGS-type method for unconstrained non-convex minimization. (English) Zbl 1128.65040 J. Appl. Math. Comput. 24, No. 1-2, 325-331 (2007). MSC: 65K05 90C26 PDF BibTeX XML Cite \textit{Q. Guo} and \textit{J. Liu}, J. Appl. Math. Comput. 24, No. 1--2, 325--331 (2007; Zbl 1128.65040) Full Text: DOI OpenURL
Yin, Hong Xia; Du, Dong Lei The global convergence of self-scaling BFGS algorithm with non-monotone line search for unconstrained nonconvex optimization problems. (English) Zbl 1125.90051 Acta Math. Sin., Engl. Ser. 23, No. 7, 1233-1240 (2007). Reviewer: David Bulger (Sydney) MSC: 90C30 90C53 PDF BibTeX XML Cite \textit{H. X. Yin} and \textit{D. L. Du}, Acta Math. Sin., Engl. Ser. 23, No. 7, 1233--1240 (2007; Zbl 1125.90051) Full Text: DOI OpenURL
Ge, Ren-Dong; Xia, Zun-Quan; Guo, Qiang A type of modified BFGS algorithm with any rank defects and the local \(Q\)-superlinear convergence properties. (English) Zbl 1110.65050 J. Appl. Math. Comput. 22, No. 1-2, 193-208 (2006). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C55 65H10 65F10 PDF BibTeX XML Cite \textit{R.-D. Ge} et al., J. Appl. Math. Comput. 22, No. 1--2, 193--208 (2006; Zbl 1110.65050) Full Text: DOI OpenURL
Andrei, Neculai An acceleration of gradient descent algorithm with backtracking for unconstrained optimization. (English) Zbl 1101.65058 Numer. Algorithms 42, No. 1, 63-73 (2006). Reviewer: Efstratios Rappos (Athens) MSC: 65K05 90C25 PDF BibTeX XML Cite \textit{N. Andrei}, Numer. Algorithms 42, No. 1, 63--73 (2006; Zbl 1101.65058) Full Text: DOI OpenURL
Kao, Chiang; Chen, Shih-Pin A stochastic quasi-Newton method for simulation response optimization. (English) Zbl 1125.90394 Eur. J. Oper. Res. 173, No. 1, 30-46 (2006). MSC: 90C15 90C55 90B05 PDF BibTeX XML Cite \textit{C. Kao} and \textit{S.-P. Chen}, Eur. J. Oper. Res. 173, No. 1, 30--46 (2006; Zbl 1125.90394) Full Text: DOI OpenURL
Zhang, Zhong-Zhi; Cao, Ding-Hua; Zeng, Jin-Ping Convergence property of a class of variable metric methods. (English) Zbl 1133.90419 Appl. Math. Lett. 17, No. 4, 437-442 (2004). MSC: 90C55 65H10 PDF BibTeX XML Cite \textit{Z.-Z. Zhang} et al., Appl. Math. Lett. 17, No. 4, 437--442 (2004; Zbl 1133.90419) Full Text: DOI OpenURL
Liu, Jian-Guo; Guo, Qiang Global convergence properties of the modified BFGS method associating with general line search model. (English) Zbl 1065.65077 J. Appl. Math. Comput. 16, No. 1-2, 195-205 (2004). Reviewer: Nicolae Popovici (Cluj-Napoca) MSC: 65K05 90C26 PDF BibTeX XML Cite \textit{J.-G. Liu} and \textit{Q. Guo}, J. Appl. Math. Comput. 16, No. 1--2, 195--205 (2004; Zbl 1065.65077) Full Text: DOI OpenURL
Pu, Dingguo; Tian, Weiwen The revised DFP algorithm without exact line search. (English) Zbl 1029.65066 J. Comput. Appl. Math. 154, No. 2, 319-339 (2003). Reviewer: N.Djuranović-Miličić (Beograd) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{D. Pu} and \textit{W. Tian}, J. Comput. Appl. Math. 154, No. 2, 319--339 (2003; Zbl 1029.65066) Full Text: DOI OpenURL
Di Fiore, Carmine; Lepore, Filomena; Zellini, Paolo Hartley-type algebras in displacement and optimization strategies. (English) Zbl 1044.65050 Linear Algebra Appl. 366, 215-232 (2003). Reviewer: Otu Vaarmann (Tallinn) MSC: 65K05 90C05 90C30 90C53 65F35 PDF BibTeX XML Cite \textit{C. Di Fiore} et al., Linear Algebra Appl. 366, 215--232 (2003; Zbl 1044.65050) Full Text: DOI OpenURL
Al-Baali, M. Extra-updates criterion for the limited memory BFGS algorithm for large scale nonlinear optimization. (English) Zbl 1005.65063 J. Complexity 18, No. 2, 557-572 (2002). MSC: 65K05 90C30 90C06 90C53 PDF BibTeX XML Cite \textit{M. Al-Baali}, J. Complexity 18, No. 2, 557--572 (2002; Zbl 1005.65063) Full Text: DOI OpenURL
Pu, Dinguo Convergence of the DFP algorithm without exact line search. (English) Zbl 0993.65071 J. Optimization Theory Appl. 112, No. 1, 187-211 (2002). Reviewer: N.Djuranović-Miličić (Beograd) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{D. Pu}, J. Optim. Theory Appl. 112, No. 1, 187--211 (2002; Zbl 0993.65071) Full Text: DOI OpenURL
Zhang, Jianzhong; Xu, Chengxian Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations. (English) Zbl 1001.65065 J. Comput. Appl. Math. 137, No. 2, 269-278 (2001). Reviewer: Berwin A.Turlach (Crawley) MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{J. Zhang} and \textit{C. Xu}, J. Comput. Appl. Math. 137, No. 2, 269--278 (2001; Zbl 1001.65065) Full Text: DOI OpenURL
Pu, Dingguo Superlinear convergence of the DFP algorithm without exact line search. (English) Zbl 1002.90068 Acta Math. Appl. Sin., Engl. Ser. 17, No. 3, 430-432 (2001). MSC: 90C30 90C53 PDF BibTeX XML Cite \textit{D. Pu}, Acta Math. Appl. Sin., Engl. Ser. 17, No. 3, 430--432 (2001; Zbl 1002.90068) Full Text: DOI OpenURL
Al-Baali, M. On the behaviour of a combined extra-updating/self-scaling BFGS method. (English) Zbl 1012.65061 J. Comput. Appl. Math. 134, No. 1-2, 269-281 (2001). Reviewer: S.Zlobec (Montreal) MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{M. Al-Baali}, J. Comput. Appl. Math. 134, No. 1--2, 269--281 (2001; Zbl 1012.65061) Full Text: DOI OpenURL
Li, Donghui; Fukushima, Masao A modified BFGS method and its global convergence in nonconvex minimization. (English) Zbl 0984.65055 J. Comput. Appl. Math. 129, No. 1-2, 15-35 (2001). Reviewer: J.Lovíšek (Bratislava) MSC: 65K05 90C26 PDF BibTeX XML Cite \textit{D. Li} and \textit{M. Fukushima}, J. Comput. Appl. Math. 129, No. 1--2, 15--35 (2001; Zbl 0984.65055) Full Text: DOI OpenURL
Pu, Dingguo The convergence of Broyden algorithms for LC gradient function. (English) Zbl 0962.90046 Acta Math. Appl. Sin., Engl. Ser. 16, No. 3, 313-319 (2000). Reviewer: Werner H.Schmidt (Greifswald) MSC: 90C30 PDF BibTeX XML Cite \textit{D. Pu}, Acta Math. Appl. Sin., Engl. Ser. 16, No. 3, 313--319 (2000; Zbl 0962.90046) Full Text: DOI OpenURL
Zeng, Qingguang; He, Guoping; Wu, Fang A robust superlinearly convergent algorithm for linearly constrained optimization problems under degeneracy. (English) Zbl 0948.90119 Acta Math. Appl. Sin., Engl. Ser. 14, No. 4, 363-373 (1998). MSC: 90C25 PDF BibTeX XML Cite \textit{Q. Zeng} et al., Acta Math. Appl. Sin., Engl. Ser. 14, No. 4, 363--373 (1998; Zbl 0948.90119) Full Text: DOI OpenURL
Hack, Michael Transformation of uniformly distributed particle ensembles. (English) Zbl 0914.11045 J. Comput. Appl. Math. 83, No. 1, 87-113 (1997). Reviewer: R.F.Tichy (Graz) MSC: 11K36 65C10 11K45 PDF BibTeX XML Cite \textit{M. Hack}, J. Comput. Appl. Math. 83, No. 1, 87--113 (1997; Zbl 0914.11045) Full Text: DOI OpenURL
Auslender, A. How to deal with the unbounded in optimization: Theory and algorithms. (English) Zbl 0887.90131 Math. Program. 79, No. 1-3 (B), 3-18 (1997). MSC: 90C25 49J52 PDF BibTeX XML Cite \textit{A. Auslender}, Math. Program. 79, No. 1--3 (B), 3--18 (1997; Zbl 0887.90131) Full Text: DOI OpenURL
Lemaréchal, Claude; Sagastizábal, Claudia Variable metric bundle methods: From conceptual to implementable forms. (English) Zbl 0872.90072 Math. Program. 76, No. 3 (B), 393-410 (1997). MSC: 90C25 65K05 90C30 PDF BibTeX XML Cite \textit{C. Lemaréchal} and \textit{C. Sagastizábal}, Math. Program. 76, No. 3 (B), 393--410 (1997; Zbl 0872.90072) Full Text: DOI OpenURL
Shi, Yixun A globalization procedure for solving nonlinear systems of equations. (English) Zbl 0861.65048 Numer. Algorithms 12, No. 3-4, 273-286 (1996). Reviewer: V.Berinde (Baia Mare) MSC: 65H10 PDF BibTeX XML Cite \textit{Y. Shi}, Numer. Algorithms 12, No. 3--4, 273--286 (1996; Zbl 0861.65048) Full Text: DOI OpenURL
Fei, Pusheng; Chen, Zhong An improved quasi-Newton method for unconstrained optimization. (English) Zbl 0919.49021 Wuhan Univ. J. Nat. Sci. 1, No. 1, 35-37 (1996). MSC: 49M15 PDF BibTeX XML Cite \textit{P. Fei} and \textit{Z. Chen}, Wuhan Univ. J. Nat. Sci. 1, No. 1, 35--37 (1996; Zbl 0919.49021) Full Text: DOI OpenURL
Denton, James W.; Hung, Ming S. A comparison of nonlinear optimization methods for supervised learning in multilayer feedforward neural networks. (English) Zbl 0912.90253 Eur. J. Oper. Res. 93, No. 2, 358-368 (1996). MSC: 90C30 68T05 68T10 PDF BibTeX XML Cite \textit{J. W. Denton} and \textit{M. S. Hung}, Eur. J. Oper. Res. 93, No. 2, 358--368 (1996; Zbl 0912.90253) Full Text: DOI OpenURL
Potra, F. A.; Shi, Y. Efficent line search algorithm for unconstrained optimization. (English) Zbl 0831.90106 J. Optimization Theory Appl. 85, No. 3, 677-704 (1995). MSC: 90C30 PDF BibTeX XML Cite \textit{F. A. Potra} and \textit{Y. Shi}, J. Optim. Theory Appl. 85, No. 3, 677--704 (1995; Zbl 0831.90106) Full Text: DOI OpenURL
Chen, Z.; Fei, P.; Zheng, H. A parallel quasi-Newton algorithm for unconstrained optimization. (English) Zbl 0827.49022 Computing 55, No. 2, 125-133 (1995). MSC: 49M37 90C30 PDF BibTeX XML Cite \textit{Z. Chen} et al., Computing 55, No. 2, 125--133 (1995; Zbl 0827.49022) Full Text: DOI OpenURL
Yuan, Yaxiang; Stoer, J. A subspace study on conjugate gradient algorithms. (English) Zbl 0823.65061 Z. Angew. Math. Mech. 75, No. 1, 69-77 (1995). Reviewer: Johannes Terno (Dresden) MSC: 65K05 90C30 90C52 PDF BibTeX XML Cite \textit{Y. Yuan} and \textit{J. Stoer}, Z. Angew. Math. Mech. 75, No. 1, 69--77 (1995; Zbl 0823.65061) Full Text: DOI OpenURL
Bonnans, J. F.; Gilbert, J. Ch.; Lemaréchal, C.; Sagastizábal, C. A. A family of variable metric proximal methods. (English) Zbl 0832.90102 Math. Program. 68, No. 1 (A), 15-47 (1995). MSC: 90C30 65K05 52A41 90C25 49J52 PDF BibTeX XML Cite \textit{J. F. Bonnans} et al., Math. Program. 68, No. 1 (A), 15--47 (1995; Zbl 0832.90102) Full Text: DOI OpenURL
Hu, Y. F.; Storey, C. Family of optimally conditioned quasi-Newton updates for unconstrained optimization. (English) Zbl 0821.90103 J. Optimization Theory Appl. 83, No. 2, 421-431 (1994). Reviewer: Deng Naiyang (Beijing) MSC: 90C30 PDF BibTeX XML Cite \textit{Y. F. Hu} and \textit{C. Storey}, J. Optim. Theory Appl. 83, No. 2, 421--431 (1994; Zbl 0821.90103) Full Text: DOI OpenURL
Siegel, Dirk Modifying the BFGS update by a new column scaling technique. (English) Zbl 0834.90126 Math. Program. 66, No. 1 (A), 45-78 (1994). Reviewer: D.I.Duca (Cluj-Napoca) MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{D. Siegel}, Math. Program. 66, No. 1 (A), 45--78 (1994; Zbl 0834.90126) Full Text: DOI OpenURL
Nocedal, Jorge; Yuan, Yaxiang Analysis of a self-scaling quasi-Newton method. (English) Zbl 0794.90067 Math. Program. 61, No. 1 (A), 19-37 (1993). MSC: 90C30 90-08 PDF BibTeX XML Cite \textit{J. Nocedal} and \textit{Y. Yuan}, Math. Program. 61, No. 1 (A), 19--37 (1993; Zbl 0794.90067) Full Text: DOI OpenURL
Wu, Shiquan; Wu, Fang New algorithms for linear programming. (English) Zbl 0762.90054 Acta Math. Appl. Sin., Engl. Ser. 8, No. 1, 18-26 (1992). Reviewer: K.Zimmermann (Praha) MSC: 90C05 90C25 90C30 PDF BibTeX XML Cite \textit{S. Wu} and \textit{F. Wu}, Acta Math. Appl. Sin., Engl. Ser. 8, No. 1, 18--26 (1992; Zbl 0762.90054) Full Text: DOI OpenURL
Byrd, Richard H.; Nocedal, Jorge An analysis of reduced Hessian methods for constrained optimization. (English) Zbl 0719.90071 Math. Program., Ser. A 49, No. 3, 285-323 (1991). MSC: 90C30 49M15 65K05 49M30 90-08 90C20 PDF BibTeX XML Cite \textit{R. H. Byrd} and \textit{J. Nocedal}, Math. Program. 49, No. 3 (A), 285--323 (1991; Zbl 0719.90071) Full Text: DOI OpenURL
Griewank, Andreas; Jongen, Hubertus Th.; Kwong, Man Kam The equivalence of strict convexity and injectivity of the gradient in bounded level sets. (English) Zbl 0738.49012 Math. Program., Ser. A 51, No. 2, 273-278 (1991). Reviewer: J.Thierfelder (Ilmenau) MSC: 49J52 52A41 26B25 PDF BibTeX XML Cite \textit{A. Griewank} et al., Math. Program. 51, No. 2 (A), 273--278 (1991; Zbl 0738.49012) Full Text: DOI OpenURL
Griewank, Andreas The global convergence of partitioned BFGS on problems with convex decompositions and Lipschitzian gradients. (English) Zbl 0736.90068 Math. Program., Ser. A 50, No. 2, 141-175 (1991). Reviewer: A.Swift (Palmerston North) MSC: 90C30 90-08 65K05 PDF BibTeX XML Cite \textit{A. Griewank}, Math. Program. 50, No. 2 (A), 141--175 (1991; Zbl 0736.90068) Full Text: DOI OpenURL
Xu, C. X. Hybrid method for nonlinear least-square problems without calculating derivatives. (English) Zbl 0677.90065 J. Optimization Theory Appl. 65, No. 3, 555-574 (1990). Reviewer: C.X.Xu MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{C. X. Xu}, J. Optim. Theory Appl. 65, No. 3, 555--574 (1990; Zbl 0677.90065) Full Text: DOI OpenURL
Liu, Dong C.; Nocedal, Jorge On the limited memory BFGS method for large scale optimization. (English) Zbl 0696.90048 Math. Program., Ser. B 45, No. 3, 503-528 (1989). Reviewer: K.Schittkowski MSC: 90C30 90C06 65K05 90C52 PDF BibTeX XML Cite \textit{D. C. Liu} and \textit{J. Nocedal}, Math. Program. 45, No. 3 (B), 503--528 (1989; Zbl 0696.90048) Full Text: DOI OpenURL
Byrd, Richard H.; Schnabel, Robert B.; Shultz, Gerald A. Parallel quasi-Newton methods for unconstrained optimization. (English) Zbl 0665.90085 Math. Program., Ser. B 42, No. 2, 273-306 (1988). MSC: 90C30 49M15 65K05 49M37 PDF BibTeX XML Cite \textit{R. H. Byrd} et al., Math. Program. 42, No. 2 (B), 273--306 (1988; Zbl 0665.90085) Full Text: DOI OpenURL
Gilbert, Jean Charles Mise a jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d’égalité. (Updating for the metric in the reduced quasi-Newton methods in optimization with equality constraints). (French) Zbl 0657.65087 RAIRO, Modélisation Math. Anal. Numér. 22, No. 2, 251-288 (1988). Reviewer: T.F.Coleman MSC: 65K05 65H10 90C30 PDF BibTeX XML Cite \textit{J. C. Gilbert}, RAIRO, Modélisation Math. Anal. Numér. 22, No. 2, 251--288 (1988; Zbl 0657.65087) Full Text: DOI EuDML OpenURL
Zhang, Yin; Tewarson, R. P. A new quasi-Newton algorithm. (English) Zbl 0632.65076 Appl. Math. Lett. 1, No. 1, 101-104 (1988). Reviewer: F.Luban MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{R. P. Tewarson}, Appl. Math. Lett. 1, No. 1, 101--104 (1988; Zbl 0632.65076) Full Text: DOI OpenURL
Toint, Ph. L. Global convergence of the partitioned BFGS algorithm for convex partially separable optimization. (English) Zbl 0626.90076 Math. Program. 36, 290-306 (1986). Reviewer: H.Tuy MSC: 90C30 90C25 65K05 49M37 PDF BibTeX XML Cite \textit{Ph. L. Toint}, Math. Program. 36, 290--306 (1986; Zbl 0626.90076) Full Text: DOI OpenURL
de Leone, Renato; Gaudioso, Manlio Stopping criteria for linesearch methods without derivatives. (English) Zbl 0576.90087 Math. Program. 30, 285-300 (1984). MSC: 90C30 49M37 65K05 PDF BibTeX XML Cite \textit{R. de Leone} and \textit{M. Gaudioso}, Math. Program. 30, 285--300 (1984; Zbl 0576.90087) Full Text: DOI OpenURL
Gui, Xiangyun; Du, Dingzhu [Kwei, Hsiangyuin] A superlinearly convergent method to linearly constrained optimization problems under degeneracy. (English) Zbl 0564.90065 Acta Math. Appl. Sin., Engl. Ser. 1, 76-84 (1984). MSC: 90C30 49M37 65K05 PDF BibTeX XML Cite \textit{X. Gui} and \textit{D. Du}, Acta Math. Appl. Sin., Engl. Ser. 1, 76--84 (1984; Zbl 0564.90065) Full Text: DOI OpenURL
Stoer, Josef The convergence of matrices generated by rank-2 methods from the restricted \(\beta\)-class of Broyden. (English) Zbl 0523.65047 Numer. Math. 44, 37-52 (1984). MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{J. Stoer}, Numer. Math. 44, 37--52 (1984; Zbl 0523.65047) Full Text: DOI EuDML OpenURL
Ge, Renpu; Powell, M. J. D. The convergence of variable metric matrices in unconstrained optimization. (English) Zbl 0532.49015 Math. Program. 27, 123-143 (1983). Reviewer: E.Sachs MSC: 49M15 65K05 90C30 PDF BibTeX XML Cite \textit{R. Ge} and \textit{M. J. D. Powell}, Math. Program. 27, 123--143 (1983; Zbl 0532.49015) Full Text: DOI OpenURL
Griewank, A.; Toint, Ph. L. Local convergence analysis for partitioned quasi-Newton updates. (English) Zbl 0505.65018 Numer. Math. 39, 429-448 (1982). MSC: 65K05 65H10 90C30 PDF BibTeX XML Cite \textit{A. Griewank} and \textit{Ph. L. Toint}, Numer. Math. 39, 429--448 (1982; Zbl 0505.65018) Full Text: DOI EuDML OpenURL
Griewank, A.; Toint, Ph. L. Partitioned variable metric updates for large structured optimization problems. (English) Zbl 0482.65035 Numer. Math. 39, 119-137 (1982). MSC: 65K05 90C20 PDF BibTeX XML Cite \textit{A. Griewank} and \textit{Ph. L. Toint}, Numer. Math. 39, 119--137 (1982; Zbl 0482.65035) Full Text: DOI EuDML OpenURL
Sisser, F. S. A modified Newton’s method for minimizing factorable functions. (English) Zbl 0471.49032 J. Optimization Theory Appl. 38, 461-482 (1982). MSC: 49M37 49M15 49M27 PDF BibTeX XML Cite \textit{F. S. Sisser}, J. Optim. Theory Appl. 38, 461--482 (1982; Zbl 0471.49032) Full Text: DOI OpenURL
Gabay, D. Minimizing a differentiable function over a differential manifold. (English) Zbl 0458.90060 J. Optimization Theory Appl. 37, 177-219 (1982). MSC: 90C30 90C52 53C20 53C22 PDF BibTeX XML Cite \textit{D. Gabay}, J. Optim. Theory Appl. 37, 177--219 (1982; Zbl 0458.90060) Full Text: DOI OpenURL