Bozântan, Andrei; Berinde, Vasile A comparative study of the PL homotopy and BFGS methods for some nonsmooth optimization problems. (English) Zbl 07238290 Creat. Math. Inform. 28, No. 2, 97-104 (2019). MSC: 47H10 47J25 49M15 49M99 PDF BibTeX XML Cite \textit{A. Bozântan} and \textit{V. Berinde}, Creat. Math. Inform. 28, No. 2, 97--104 (2019; Zbl 07238290)
Brust, Johannes J.; Marcia, Roummel F.; Petra, Cosmin G. Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints. (English) Zbl 1435.90147 Comput. Optim. Appl. 74, No. 3, 669-701 (2019). MSC: 90C53 90C06 PDF BibTeX XML Cite \textit{J. J. Brust} et al., Comput. Optim. Appl. 74, No. 3, 669--701 (2019; Zbl 1435.90147) Full Text: DOI
Liu, Li BFGS algorithm by using the decomposition matrix of the correction matrix to obtain the search direction. (Chinese. English summary) Zbl 1374.90363 J. Math., Wuhan Univ. 36, No. 5, 1035-1039 (2016). MSC: 90C30 90C53 PDF BibTeX XML Cite \textit{L. Liu}, J. Math., Wuhan Univ. 36, No. 5, 1035--1039 (2016; Zbl 1374.90363)
Periçaro, G. A.; Santos, S. R.; Ribeiro, A. A.; Matioli, L. C. HLRF-BFGS optimization algorithm for structural reliability. (English) Zbl 1443.90158 Appl. Math. Modelling 39, No. 7, 2025-2035 (2015). MSC: 90B25 90C53 PDF BibTeX XML Cite \textit{G. A. Periçaro} et al., Appl. Math. Modelling 39, No. 7, 2025--2035 (2015; Zbl 1443.90158) Full Text: DOI
Tarzanagh, D. Ataee; Peyghami, M. Reza A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems. (English) Zbl 1337.90043 J. Glob. Optim. 63, No. 4, 709-728 (2015). MSC: 90C06 90C59 PDF BibTeX XML Cite \textit{D. A. Tarzanagh} and \textit{M. R. Peyghami}, J. Glob. Optim. 63, No. 4, 709--728 (2015; Zbl 1337.90043) Full Text: DOI
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
Andrei, Neculai A simple three-term conjugate gradient algorithm for unconstrained optimization. (English) Zbl 1258.65056 J. Comput. Appl. Math. 241, 19-29 (2013). MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{N. Andrei}, J. Comput. Appl. Math. 241, 19--29 (2013; Zbl 1258.65056) Full Text: DOI
Gejadze, I. Yu.; Le Dimet, F.-X.; Shutyaev, V. On optimal solution error covariances in variational data assimilation problems. (English) Zbl 1185.65106 J. Comput. Phys. 229, No. 6, 2159-2178 (2010). MSC: 65K10 49J20 49M15 PDF BibTeX XML Cite \textit{I. Yu. Gejadze} et al., J. Comput. Phys. 229, No. 6, 2159--2178 (2010; Zbl 1185.65106) Full Text: DOI
Zhang, Jing A new nonmonotone line search BFGS algorithm. (Chinese. English summary) Zbl 1212.90412 J. Hebei Norm. Univ., Nat. Sci. Ed. 33, No. 3, 299-303 (2009). MSC: 90C53 90C30 65K05 PDF BibTeX XML Cite \textit{J. Zhang}, J. Hebei Norm. Univ., Nat. Sci. Ed. 33, No. 3, 299--303 (2009; Zbl 1212.90412)
Sahari, M. L.; Khaldi, R. Quasi-Newton type of diagonal updating for the L-BFGS method. (English) Zbl 1199.65210 Acta Math. Univ. Comen., New Ser. 78, No. 2, 173-181 (2009). Reviewer: Ján Lovíšek (Bratislava) MSC: 65K05 90C53 90C25 65Y20 PDF BibTeX XML Cite \textit{M. L. Sahari} and \textit{R. Khaldi}, Acta Math. Univ. Comen., New Ser. 78, No. 2, 173--181 (2009; Zbl 1199.65210) Full Text: EuDML
Reed, M. B. L-Broyden methods: a generalization of the L-BFGS method to the limited-memory Broyden family. (English) Zbl 1165.65032 Int. J. Comput. Math. 86, No. 4, 606-615 (2009). MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{M. B. Reed}, Int. J. Comput. Math. 86, No. 4, 606--615 (2009; Zbl 1165.65032) Full Text: DOI Link
Gejadze, I. Yu.; Le Dimet, F.-X.; Shutyaev, V. On analysis error covariances in variational data assimilation. (English) Zbl 1168.65357 SIAM J. Sci. Comput. 30, No. 4, 847-1874 (2008). MSC: 65K10 49K20 49M15 PDF BibTeX XML Cite \textit{I. Yu. Gejadze} et al., SIAM J. Sci. Comput. 30, No. 4, p1847--1874 (2008; Zbl 1168.65357) Full Text: DOI
Wang, Haibin A class of modified BFGS algorithm with superlinear convergence based on new quasi-Newton equation. (Chinese. English summary) Zbl 1150.90527 J. Lanzhou Univ. Technol. 33, No. 4, 150-152 (2007). MSC: 90C53 PDF BibTeX XML Cite \textit{H. Wang}, J. Lanzhou Univ. Technol. 33, No. 4, 150--152 (2007; Zbl 1150.90527)
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
Guo, Qiang; Liu, Jian-guo Global convergence properties of two modified BFGS-type methods. (English) Zbl 1125.65048 J. Appl. Math. Comput. 23, No. 1-2, 311-319 (2007). Reviewer: Jiří Vaníček (Praha) MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{Q. Guo} and \textit{J.-g. Liu}, J. Appl. Math. Comput. 23, No. 1--2, 311--319 (2007; Zbl 1125.65048) Full Text: DOI
Wu, Ting; Sun, Linping A quasi-Newton based pattern search algorithm for unconstrained optimization. (English) Zbl 1110.65052 Appl. Math. Comput. 183, No. 1, 685-694 (2006). Reviewer: Efstratios Rappos (Athens) MSC: 65K05 90C53 90C56 90C30 PDF BibTeX XML Cite \textit{T. Wu} and \textit{L. Sun}, Appl. Math. Comput. 183, No. 1, 685--694 (2006; Zbl 1110.65052) Full Text: DOI
Di Fiore, Carmine; Fanelli, Stefano; Zellini, Paolo Low-complexity minimization algorithms. (English) Zbl 1164.65422 Numer. Linear Algebra Appl. 12, No. 8, 755-768 (2005). Reviewer: Jan Chleboun (Praha) MSC: 65K05 90C53 65Y20 90C30 PDF BibTeX XML Cite \textit{C. Di Fiore} et al., Numer. Linear Algebra Appl. 12, No. 8, 755--768 (2005; Zbl 1164.65422) Full Text: DOI
Al-Baali, M. Quasi-Newton algorithms for large-scale nonlinear least-squares. (English) Zbl 1066.90139 Di Pillo, Gianni (ed.) et al., High performance algorithms and software for nonlinear optimization. Selected lectures presented at the workshop, Erice, Italy, June 30–July 8, 2001. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7532-4/hbk). Appl. Optim. 82, 1-21 (2003). MSC: 90C53 90C06 PDF BibTeX XML Cite \textit{M. Al-Baali}, Appl. Optim. 82, 1--21 (2003; Zbl 1066.90139)
Armand, Paul A quasi-Newton penalty barrier method for convex minimization problems. (English) Zbl 1053.90106 Comput. Optim. Appl. 26, No. 1, 5-34 (2003). MSC: 90C25 90C53 49M30 90C51 PDF BibTeX XML Cite \textit{P. Armand}, Comput. Optim. Appl. 26, No. 1, 5--34 (2003; Zbl 1053.90106) Full Text: DOI
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
Ford, J. A.; Tharmlikit, S. New implicit updates in multi-step quasi-Newton methods for unconstrained optimisation. (English) Zbl 1025.65035 J. Comput. Appl. Math. 152, No. 1-2, 133-146 (2003). MSC: 65K05 90C53 90C30 PDF BibTeX XML Cite \textit{J. A. Ford} and \textit{S. Tharmlikit}, J. Comput. Appl. Math. 152, No. 1--2, 133--146 (2003; Zbl 1025.65035) Full Text: DOI
Armand, Paul; Gilbert, J. Charles; Jan-Jégou, Sophie A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach. (English) Zbl 1008.90045 Math. Program. 92, No. 3 (B), 393-424 (2002). MSC: 90C25 90C51 90C53 65K05 PDF BibTeX XML Cite \textit{P. Armand} et al., Math. Program. 92, No. 3 (B), 393--424 (2002; Zbl 1008.90045) Full Text: DOI
Ramos, A. M.; Glowinski, R.; Periaux, J. Pointwise control of the Burgers equation and related Nash equilibrium problems: Computational approach. (English) Zbl 1027.49020 J. Optimization Theory Appl. 112, No. 3, 499-516 (2002). MSC: 49K20 35Q53 91A10 90C29 90C52 49M25 PDF BibTeX XML Cite \textit{A. M. Ramos} et al., J. Optim. Theory Appl. 112, No. 3, 499--516 (2002; Zbl 1027.49020) Full Text: DOI
Armand, Paul; Gilbert, Jean Charles; Jan-Jégou, Sophie A feasible BFGS interior point algorithm for solving convex minimization problems. (English) Zbl 0990.90092 SIAM J. Optim. 11, No. 1, 199-222 (2000). MSC: 90C25 90C51 90C53 PDF BibTeX XML Cite \textit{P. Armand} et al., SIAM J. Optim. 11, No. 1, 199--222 (2000; Zbl 0990.90092) Full Text: DOI
Armand, Paul; Gilbert, J. Charles A piecewise line-search technique for maintaining the positive definiteness of the matrices in the SQP method. (English) Zbl 0963.90059 Comput. Optim. Appl. 16, No. 2, 121-158 (2000). MSC: 90C30 90C55 PDF BibTeX XML Cite \textit{P. Armand} and \textit{J. C. Gilbert}, Comput. Optim. Appl. 16, No. 2, 121--158 (2000; Zbl 0963.90059) Full Text: DOI
Choi, T. D.; Kelley, C. T. Superlinear convergence and implicit filtering. (English) Zbl 0994.65071 SIAM J. Optim. 10, No. 4, 1149-1162 (2000). MSC: 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{T. D. Choi} and \textit{C. T. Kelley}, SIAM J. Optim. 10, No. 4, 1149--1162 (2000; Zbl 0994.65071) Full Text: DOI
Gilbert, Jean Charles Piecewise line-search techniques for constrained minimization by quasi-Newton algorithms. (English) Zbl 0909.90238 Yuan, Ya-xiang (ed.), Advances in nonlinear programming. Proceedings of the 96 international conference. Beijing, China, September 2–5, 1996. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 14, 73-103 (1998). MSC: 90C30 PDF BibTeX XML Cite \textit{J. C. Gilbert}, Appl. Optim. 14, 73--103 (1998; Zbl 0909.90238)
Liu, G.; Han, J.; Sun, D. Global convergence of the BFGS algorithm with nonmonotone linesearch. (English) Zbl 0858.90122 Optimization 34, No. 2, 147-159 (1995). MSC: 90C30 PDF BibTeX XML Cite \textit{G. Liu} et al., Optimization 34, No. 2, 147--159 (1995; Zbl 0858.90122) Full Text: DOI
Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge; Zhu, Ciyou A limited memory algorithm for bound constrained optimization. (English) Zbl 0836.65080 SIAM J. Sci. Comput. 16, No. 5, 1190-1208 (1995). Reviewer: F.Luban (Bucureşti) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{R. H. Byrd} et al., SIAM J. Sci. Comput. 16, No. 5, 1190--1208 (1995; Zbl 0836.65080) Full Text: DOI
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
Fletcher, R. An optimal positive definite update for sparse Hessian matrices. (English) Zbl 0824.65038 SIAM J. Optim. 5, No. 1, 192-218 (1995). Reviewer: K.Schittkowski (Bayreuth) MSC: 65K05 90C30 90C06 PDF BibTeX XML Cite \textit{R. Fletcher}, SIAM J. Optim. 5, No. 1, 192--218 (1995; Zbl 0824.65038) Full Text: DOI
Saadallah, Adel F. A quasi-Newton method using a nonquadratic model. (English) Zbl 0810.65057 J. Comput. Appl. Math. 51, No. 3, 327-338 (1994). Reviewer: J.F.Bonnans (Le Chesnay) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{A. F. Saadallah}, J. Comput. Appl. Math. 51, No. 3, 327--338 (1994; Zbl 0810.65057) Full Text: DOI
Lardner, R. W. Optimal control of open boundary conditions for a numerical tidal model. (English) Zbl 0767.76036 Comput. Methods Appl. Mech. Eng. 102, No. 3, 367-387 (1993). MSC: 76M20 76B15 86A05 PDF BibTeX XML Cite \textit{R. W. Lardner}, Comput. Methods Appl. Mech. Eng. 102, No. 3, 367--387 (1993; Zbl 0767.76036) Full Text: DOI
Yuan, Yaxiang A modified BFGS algorithm for unconstrained optimization. (English) Zbl 0733.65039 IMA J. Numer. Anal. 11, No. 3, 325-332 (1991). Reviewer: Jiří Rohn (Praha) MSC: 65K05 90C53 PDF BibTeX XML Cite \textit{Y. Yuan}, IMA J. Numer. Anal. 11, No. 3, 325--332 (1991; Zbl 0733.65039) Full Text: DOI
Xu, Huifu; Sheng, Songbai Broyden family of collinear scaling algorithm for unconstrained optimization. (English) Zbl 0759.65037 Numer. Math., Nanjing 13, No. 4, 318-330 (1991). Reviewer: S.Wright (Argonne) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{H. Xu} and \textit{S. Sheng}, Numer. Math., Nanjing 13, No. 4, 318--330 (1991; Zbl 0759.65037)
Zhang, Yin; Tewarson, R. P. Quasi-Newton algorithms with updates from the preconvex part of Broyden’s family. (English) Zbl 0661.65061 IMA J. Numer. Anal. 8, No. 4, 487-509 (1988). Reviewer: J.Rohn MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{R. P. Tewarson}, IMA J. Numer. Anal. 8, No. 4, 487--509 (1988; Zbl 0661.65061) Full Text: DOI
Gelin, J. C.; Picart, P. Use of quasi-Newton methods for large strain elastic-plastic finite element computations. (English) Zbl 0644.73067 Commun. Appl. Numer. Methods 4, No. 4, 457-469 (1988). MSC: 74S05 74B20 74-04 PDF BibTeX XML Cite \textit{J. C. Gelin} and \textit{P. Picart}, Commun. Appl. Numer. Methods 4, No. 4, 457--469 (1988; Zbl 0644.73067) Full Text: DOI
Borja, Ronaldo I. The analysis of consolidation by a quasi-Newton technique. (English) Zbl 0632.73095 Int. J. Numer. Anal. Methods Geomech. 12, No. 2, 221-229 (1988). MSC: 74L10 74S99 65F30 PDF BibTeX XML Cite \textit{R. I. Borja}, Int. J. Numer. Anal. Methods Geomech. 12, No. 2, 221--229 (1988; Zbl 0632.73095) Full Text: DOI
Bischoff, D. Indirect optimization algorithms for nonlinear contact problems. (English) Zbl 0576.73110 The mathematics of finite elements and applications V, MAFELAP 1984, proc. 5th Conf., Uxbridge/Engl. 1984, 533-545 (1985). Reviewer: H.Bufler MSC: 74A55 74M15 74S05 74P99 65K10 49M29 PDF BibTeX XML
Kamat, Manohar P.; Hayduk, Robert J. Recent developments in quasi-Newton methods for structural analysis and synthesis. (English) Zbl 0541.73109 AIAA J. 20, 672-679 (1982). MSC: 74P99 74S30 PDF BibTeX XML Cite \textit{M. P. Kamat} and \textit{R. J. Hayduk}, AIAA J. 20, 672--679 (1982; Zbl 0541.73109) Full Text: DOI