Wang, Peng; Zhu, Detong A derivative-free modified tensor method with curvilinear linesearch for unconstrained nonlinear programming. (English) Zbl 07814973 Optimization 73, No. 3, 597-621 (2024). MSC: 90C30 90C56 65K05 PDFBibTeX XMLCite \textit{P. Wang} and \textit{D. Zhu}, Optimization 73, No. 3, 597--621 (2024; Zbl 07814973) Full Text: DOI
Hare, Warren; Royer, Clément W. Detecting negative eigenvalues of exact and approximate Hessian matrices in optimization. (English) Zbl 07755339 Optim. Lett. 17, No. 8, 1739-1756 (2023). MSC: 90C26 PDFBibTeX XMLCite \textit{W. Hare} and \textit{C. W. Royer}, Optim. Lett. 17, No. 8, 1739--1756 (2023; Zbl 07755339) Full Text: DOI arXiv
Pho, Kim-Hung Improvements of the Newton-Raphson method. (English) Zbl 1484.65105 J. Comput. Appl. Math. 408, Article ID 114106, 16 p. (2022). MSC: 65H05 PDFBibTeX XMLCite \textit{K.-H. Pho}, J. Comput. Appl. Math. 408, Article ID 114106, 16 p. (2022; Zbl 1484.65105) Full Text: DOI
Fasano, Giovanni; Pesenti, Raffaele Polarity and conjugacy for quadratic hypersurfaces: a unified framework with recent advances. (English) Zbl 1454.90086 J. Comput. Appl. Math. 390, Article ID 113248, 16 p. (2021). MSC: 90C30 90C52 65K05 03H05 65F05 14P10 14N05 PDFBibTeX XMLCite \textit{G. Fasano} and \textit{R. Pesenti}, J. Comput. Appl. Math. 390, Article ID 113248, 16 p. (2021; Zbl 1454.90086) Full Text: DOI
Schaeffer, Hayden; McCalla, Scott G. Extending the step-size restriction for gradient descent to avoid strict saddle points. (English) Zbl 1484.90088 SIAM J. Math. Data Sci. 2, No. 4, 1181-1197 (2020). MSC: 90C26 37L10 PDFBibTeX XMLCite \textit{H. Schaeffer} and \textit{S. G. McCalla}, SIAM J. Math. Data Sci. 2, No. 4, 1181--1197 (2020; Zbl 1484.90088) Full Text: DOI arXiv
De Leone, Renato; Fasano, Giovanni; Roma, Massimo; Sergeyev, Yaroslav D. Iterative grossone-based computation of negative curvature directions in large-scale optimization. (English) Zbl 1450.90009 J. Optim. Theory Appl. 186, No. 2, 554-589 (2020). MSC: 90C06 90C30 65K05 PDFBibTeX XMLCite \textit{R. De Leone} et al., J. Optim. Theory Appl. 186, No. 2, 554--589 (2020; Zbl 1450.90009) Full Text: DOI
Hallak, Nadav; Teboulle, Marc Finding second-order stationary points in constrained minimization: a feasible direction approach. (English) Zbl 1450.90034 J. Optim. Theory Appl. 186, No. 2, 480-503 (2020). MSC: 90C26 90C30 65K05 90C46 90C31 PDFBibTeX XMLCite \textit{N. Hallak} and \textit{M. Teboulle}, J. Optim. Theory Appl. 186, No. 2, 480--503 (2020; Zbl 1450.90034) Full Text: DOI
Gratton, S.; Royer, C. W.; Vicente, L. N. A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds. (English) Zbl 1437.90130 Math. Program. 179, No. 1-2 (A), 195-222 (2020). MSC: 90C26 90C56 65K05 PDFBibTeX XMLCite \textit{S. Gratton} et al., Math. Program. 179, No. 1--2 (A), 195--222 (2020; Zbl 1437.90130) Full Text: DOI Link
Lee, Jason D.; Panageas, Ioannis; Piliouras, Georgios; Simchowitz, Max; Jordan, Michael I.; Recht, Benjamin First-order methods almost always avoid strict saddle points. (English) Zbl 1415.90089 Math. Program. 176, No. 1-2 (B), 311-337 (2019). MSC: 90C26 PDFBibTeX XMLCite \textit{J. D. Lee} et al., Math. Program. 176, No. 1--2 (B), 311--337 (2019; Zbl 1415.90089) Full Text: DOI arXiv
Curtis, Frank E.; Robinson, Daniel P. Exploiting negative curvature in deterministic and stochastic optimization. (English) Zbl 1417.49036 Math. Program. 176, No. 1-2 (B), 69-94 (2019). MSC: 49M05 49M15 49M37 65K05 90C15 90C26 90C30 90C53 PDFBibTeX XMLCite \textit{F. E. Curtis} and \textit{D. P. Robinson}, Math. Program. 176, No. 1--2 (B), 69--94 (2019; Zbl 1417.49036) Full Text: DOI arXiv
Wick, Thomas Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation. (English) Zbl 1439.74375 Comput. Methods Appl. Mech. Eng. 325, 577-611 (2017). MSC: 74R10 35Q74 49M15 74S05 65M60 74F10 PDFBibTeX XMLCite \textit{T. Wick}, Comput. Methods Appl. Mech. Eng. 325, 577--611 (2017; Zbl 1439.74375) Full Text: DOI
Panageas, Ioannis; Piliouras, Georgios Gradient descent only converges to minimizers: non-isolated critical points and invariant regions. (English) Zbl 1402.90210 Papadimitriou, Christos H. (ed.), 8th innovations in theoretical computer science conference, ITCS 2017, Berkeley, CA, USA, January 9–11, 2017. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-95977-029-3). LIPIcs – Leibniz International Proceedings in Informatics 67, Article 2, 12 p. (2017). MSC: 90C52 PDFBibTeX XMLCite \textit{I. Panageas} and \textit{G. Piliouras}, LIPIcs -- Leibniz Int. Proc. Inform. 67, Article 2, 12 p. (2017; Zbl 1402.90210) Full Text: DOI arXiv
Goldfarb, Donald; Mu, Cun; Wright, John; Zhou, Chaoxu Using negative curvature in solving nonlinear programs. (English) Zbl 1393.90114 Comput. Optim. Appl. 68, No. 3, 479-502 (2017). MSC: 90C30 PDFBibTeX XMLCite \textit{D. Goldfarb} et al., Comput. Optim. Appl. 68, No. 3, 479--502 (2017; Zbl 1393.90114) Full Text: DOI arXiv
Cano, Javier; Moguerza, Javier M.; Prieto, Francisco J. Using improved directions of negative curvature for the solution of bound-constrained nonconvex problems. (English) Zbl 1373.90144 J. Optim. Theory Appl. 174, No. 2, 474-499 (2017). MSC: 90C30 90C51 PDFBibTeX XMLCite \textit{J. Cano} et al., J. Optim. Theory Appl. 174, No. 2, 474--499 (2017; Zbl 1373.90144) Full Text: DOI
Gratton, S.; Royer, C. W.; Vicente, L. N. A second-order globally convergent direct-search method and its worst-case complexity. (English) Zbl 1338.90463 Optimization 65, No. 6, 1105-1128 (2016). MSC: 90C56 90C60 49M05 PDFBibTeX XMLCite \textit{S. Gratton} et al., Optimization 65, No. 6, 1105--1128 (2016; Zbl 1338.90463) Full Text: DOI Link
Steihaug, Trond; Suleiman, Sara On the final steps of Newton and higher order methods. (English) Zbl 1343.90091 Optim. Lett. 10, No. 2, 401-416 (2016). MSC: 90C30 90C53 PDFBibTeX XMLCite \textit{T. Steihaug} and \textit{S. Suleiman}, Optim. Lett. 10, No. 2, 401--416 (2016; Zbl 1343.90091) Full Text: DOI
Chen, Yannan; Sun, Wenyu A dwindling filter line search method for unconstrained optimization. (English) Zbl 1307.65085 Math. Comput. 84, No. 291, 187-208 (2015). MSC: 65K05 90C30 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{W. Sun}, Math. Comput. 84, No. 291, 187--208 (2015; Zbl 1307.65085) Full Text: DOI
Avelino, Catarina P.; Moguerza, Javier M.; Olivares, Alberto; Prieto, Francisco J. Combining and scaling descent and negative curvature directions. (English) Zbl 1227.49038 Math. Program. 128, No. 1-2 (A), 285-319 (2011). MSC: 49M37 65K05 90C30 PDFBibTeX XMLCite \textit{C. P. Avelino} et al., Math. Program. 128, No. 1--2 (A), 285--319 (2011; Zbl 1227.49038) Full Text: DOI Link
Han, Xue; Sun, Wenyu; Dang, Chuangyin Nonmonotone second-order Wolfe’s line search method for unconstrained optimization problems. (English) Zbl 1205.65200 Comput. Math. Appl. 60, No. 9, 2517-2525 (2010). MSC: 65K10 90C26 PDFBibTeX XMLCite \textit{X. Han} et al., Comput. Math. Appl. 60, No. 9, 2517--2525 (2010; Zbl 1205.65200) Full Text: DOI
Apostolopoulou, M. S.; Sotiropoulos, D. G.; Botsaris, C. A. A curvilinear method based on minimal-memory BFGS updates. (English) Zbl 1208.65081 Appl. Math. Comput. 217, No. 2, 882-892 (2010). Reviewer: Otu Vaarmann (Tallinn) MSC: 65K05 PDFBibTeX XMLCite \textit{M. S. Apostolopoulou} et al., Appl. Math. Comput. 217, No. 2, 882--892 (2010; Zbl 1208.65081) Full Text: DOI
Andreani, R.; Birgin, E. G.; Martínez, J. M.; Schuverdt, M. L. Second-order negative-curvature methods for box-constrained and general constrained optimization. (English) Zbl 1187.90265 Comput. Optim. Appl. 45, No. 2, 209-236 (2010). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{R. Andreani} et al., Comput. Optim. Appl. 45, No. 2, 209--236 (2010; Zbl 1187.90265) Full Text: DOI Link
Fasano, Giovanni; Lucidi, Stefano A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization. (English) Zbl 1180.90192 Optim. Lett. 3, No. 4, 521-535 (2009). MSC: 90C06 PDFBibTeX XMLCite \textit{G. Fasano} and \textit{S. Lucidi}, Optim. Lett. 3, No. 4, 521--535 (2009; Zbl 1180.90192) Full Text: DOI
Olivares, Alberto; Moguerza, Javier M. Improving directions of negative curvature in an efficient manner. (English) Zbl 1163.90754 Ann. Oper. Res. 166, 183-201 (2009). MSC: 90C30 PDFBibTeX XMLCite \textit{A. Olivares} and \textit{J. M. Moguerza}, Ann. Oper. Res. 166, 183--201 (2009; Zbl 1163.90754) Full Text: DOI
Zhou, Qunyan; Sun, Wenyu Adaptive nonmonotone line search method for unconstrained optimization. (English) Zbl 07759241 Front. Math. China 3, No. 1, 133-148 (2008). MSC: 65K05 90C30 PDFBibTeX XMLCite \textit{Q. Zhou} and \textit{W. Sun}, Front. Math. China 3, No. 1, 133--148 (2008; Zbl 07759241) Full Text: DOI
Fang, Haw-Ren; O’Leary, Dianne P. Modified Cholesky algorithms: A catalog with new approaches. (English) Zbl 1156.65023 Math. Program. 115, No. 2 (A), 319-349 (2008). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F05 90C30 90C35 65K05 PDFBibTeX XMLCite \textit{H.-R. Fang} and \textit{D. P. O'Leary}, Math. Program. 115, No. 2 (A), 319--349 (2008; Zbl 1156.65023) Full Text: DOI Link
Olivares, Alberto; Moguerza, Javier M.; Prieto, Francisco J. Nonconvex optimization using negative curvature within a modified linesearch. (English) Zbl 1146.90054 Eur. J. Oper. Res. 189, No. 3, 706-722 (2008). MSC: 90C26 90C53 PDFBibTeX XMLCite \textit{A. Olivares} et al., Eur. J. Oper. Res. 189, No. 3, 706--722 (2008; Zbl 1146.90054) Full Text: DOI Link
Sun, Wenyu; Zhou, Qunyan An unconstrained optimization method using nonmonotone second order Goldstein’s line search. (English) Zbl 1132.65057 Sci. China, Ser. A 50, No. 10, 1389-1400 (2007). Reviewer: Karel Zimmermann (Praha) MSC: 65K05 90C30 PDFBibTeX XMLCite \textit{W. Sun} and \textit{Q. Zhou}, Sci. China, Ser. A 50, No. 10, 1389--1400 (2007; Zbl 1132.65057) Full Text: DOI
Fasano, Giovanni; Roma, Massimo Iterative computation of negative curvature directions in large scale optimization. (English) Zbl 1171.90549 Comput. Optim. Appl. 38, No. 1, 81-104 (2007). MSC: 90C52 60K10 PDFBibTeX XMLCite \textit{G. Fasano} and \textit{M. Roma}, Comput. Optim. Appl. 38, No. 1, 81--104 (2007; Zbl 1171.90549) Full Text: DOI
Moguerza, Javier M.; Olivares, Alberto; Prieto, Francisco J. A note on the use of vector barrier parameters for interior-point methods. (English) Zbl 1131.90072 Eur. J. Oper. Res. 181, No. 2, 571-585 (2007). MSC: 90C51 90C26 PDFBibTeX XMLCite \textit{J. M. Moguerza} et al., Eur. J. Oper. Res. 181, No. 2, 571--585 (2007; Zbl 1131.90072) Full Text: DOI Link
Fasano, G. Planar conjugate gradient algorithm for large-scale unconstrained optimization. II: Application. (English) Zbl 1079.90163 J. Optimization Theory Appl. 125, No. 3, 543-558 (2005). MSC: 90C52 90C30 PDFBibTeX XMLCite \textit{G. Fasano}, J. Optim. Theory Appl. 125, No. 3, 543--558 (2005; Zbl 1079.90163) Full Text: DOI
Fasano, G. Planar conjugate gradient algorithm for large-scale unconstrained optimization. I: Theory. (English) Zbl 1079.90162 J. Optimization Theory Appl. 125, No. 3, 523-541 (2005). MSC: 90C52 90C30 PDFBibTeX XMLCite \textit{G. Fasano}, J. Optim. Theory Appl. 125, No. 3, 523--541 (2005; Zbl 1079.90162) Full Text: DOI
Conforti, D.; Mancini, M. A curvilinear search algorithm for unconstrained optimization by automatic differentiation. (English) Zbl 1103.90399 Optim. Methods Softw. 15, No. 3-4, 283-297 (2001). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{D. Conforti} and \textit{M. Mancini}, Optim. Methods Softw. 15, No. 3--4, 283--297 (2001; Zbl 1103.90399) Full Text: DOI
Jarre, Florian An interior method for nonconvex semidefinite programs. (English) Zbl 1035.90055 Optim. Eng. 1, No. 4, 347-372 (2000). MSC: 90C51 90C22 90C26 PDFBibTeX XMLCite \textit{F. Jarre}, Optim. Eng. 1, No. 4, 347--372 (2000; Zbl 1035.90055) Full Text: DOI
Zhou, W.; Chalabi, Z. S. Modifications of the Wolfe line search rules to satisfy second-order optimality conditions in unconstrained optimization. (English) Zbl 0897.90179 J. Optimization Theory Appl. 96, No. 1, 235-246 (1998). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{W. Zhou} and \textit{Z. S. Chalabi}, J. Optim. Theory Appl. 96, No. 1, 235--246 (1998; Zbl 0897.90179) Full Text: DOI
Ferris, M. C.; Lucidi, S.; Roma, M. Nonmonotone curvilinear line search methods for unconstrained optimization. (English) Zbl 0860.90111 Comput. Optim. Appl. 6, No. 2, 117-136 (1996). MSC: 90C30 PDFBibTeX XMLCite \textit{M. C. Ferris} et al., Comput. Optim. Appl. 6, No. 2, 117--136 (1996; Zbl 0860.90111) Full Text: DOI
Forsgren, Anders; Ringertz, Ulf On the use of a modified Newton method for nonlinear finite element analysis. (English) Zbl 0846.73062 Comput. Methods Appl. Mech. Eng. 110, No. 3-4, 275-283 (1993). MSC: 74S05 74P99 74K15 PDFBibTeX XMLCite \textit{A. Forsgren} and \textit{U. Ringertz}, Comput. Methods Appl. Mech. Eng. 110, No. 3--4, 275--283 (1993; Zbl 0846.73062) Full Text: DOI
Ben-Tal, A.; Melman, A.; Zowe, J. Curved search methods for unconstrained optimization. (English) Zbl 0722.90071 Optimization 21, No. 5, 669-695 (1990). Reviewer: J.-E.Martínez-Legaz (Barcelona) MSC: 90C30 90-08 65K05 90C99 PDFBibTeX XMLCite \textit{A. Ben-Tal} et al., Optimization 21, No. 5, 669--695 (1990; Zbl 0722.90071) Full Text: DOI
Otero, Manuel Zwei Trajektorienverfahren zur Lösung nichtlinearer Optimierungsaufgaben. (Two trajectory methods for the solution of nonlinear optimization problems). (German) Zbl 0714.90090 Optimization 21, No. 4, 559-573 (1990). MSC: 90C30 90-08 65D15 PDFBibTeX XMLCite \textit{M. Otero}, Optimization 21, No. 4, 559--573 (1990; Zbl 0714.90090) Full Text: DOI
Pham Dinh Tao; Wang, S.; Yassine, A. Training multi-layered neural network with a trust-region based algorithm. (English) Zbl 0707.90097 RAIRO, Modélisation Math. Anal. Numér. 24, No. 4, 523-553 (1990). MSC: 90C90 92B20 90-08 90C26 PDFBibTeX XMLCite \textit{Pham Dinh Tao} et al., RAIRO, Modélisation Math. Anal. Numér. 24, No. 4, 523--553 (1990; Zbl 0707.90097) Full Text: DOI EuDML
Nash, Stephen G. Avoiding modified matrix factorizations in Newton-like methods. (English) Zbl 0655.65091 J. Inf. Optim. Sci. 9, No. 2, 159-182 (1988). Reviewer: E.Duca MSC: 65K05 90C30 PDFBibTeX XMLCite \textit{S. G. Nash}, J. Inf. Optim. Sci. 9, No. 2, 159--182 (1988; Zbl 0655.65091) Full Text: DOI
Goodman, D. M.; Dudley, D. G. An output error model and algorithm for electromagnetic system identification. (English) Zbl 0641.93023 Circuits Syst. Signal Process. 6, 471-505 (1987). Reviewer: G.G.Vrânceanu MSC: 93B30 78A45 93C05 93B40 93C95 PDFBibTeX XMLCite \textit{D. M. Goodman} and \textit{D. G. Dudley}, Circuits Syst. Signal Process. 6, 471--505 (1987; Zbl 0641.93023) Full Text: DOI
Mikhalevich, V. S.; Redkovskij, N. N.; Perekatov, A. E. Minimization methods for functions on simple sets. (English. Russian original) Zbl 0642.65047 Cybernetics 22, No. 4, 437-449 (1986); translation from Kibernetika 1986, No. 4, 25-35 (1986). Reviewer: S.Zlobec MSC: 65K05 90C25 PDFBibTeX XMLCite \textit{V. S. Mikhalevich} et al., Cybernetics 22, No. 4, 437--449 (1986; Zbl 0642.65047); translation from Kibernetika 1986, No. 4, 25--35 (1986) Full Text: DOI
Gould, Nicholas I. M. On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem. (English) Zbl 0591.90068 Math. Program. 32, 90-99 (1985). Reviewer: I.Kaneko MSC: 90C20 65K05 PDFBibTeX XMLCite \textit{N. I. M. Gould}, Math. Program. 32, 90--99 (1985; Zbl 0591.90068) Full Text: DOI
Bulteau, J. P.; Vial, J. P. A restricted trust region algorithm for unconstrained optimization. (English) Zbl 0556.90075 J. Optimization Theory Appl. 47, 413-435 (1985). MSC: 90C30 49M37 65K05 PDFBibTeX XMLCite \textit{J. P. Bulteau} and \textit{J. P. Vial}, J. Optim. Theory Appl. 47, 413--435 (1985; Zbl 0556.90075) Full Text: DOI
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 PDFBibTeX XMLCite \textit{D. Gabay}, J. Optim. Theory Appl. 37, 177--219 (1982; Zbl 0458.90060) Full Text: DOI
Murray, Daniel M.; Yakowitz, Sidney J. The application of optimal control methodology to nonlinear programming problems. (English) Zbl 0476.90063 Math. Program. 21, 331-347 (1981). MSC: 90C30 90C39 49L20 49M37 65K05 93C55 PDFBibTeX XMLCite \textit{D. M. Murray} and \textit{S. J. Yakowitz}, Math. Program. 21, 331--347 (1981; Zbl 0476.90063) Full Text: DOI
Goldfarb, Donald Curvilinear path steplength algorithms for minimization which use directions of negative curvature. (English) Zbl 0428.90068 Math. Program. 18, 31-40 (1980). MSC: 90C30 65K05 90C52 PDFBibTeX XMLCite \textit{D. Goldfarb}, Math. Program. 18, 31--40 (1980; Zbl 0428.90068) Full Text: DOI
Shanno, D. F. On variable-metric methods for sparse Hessians. (English) Zbl 0424.65027 Math. Comput. 34, 499-514 (1980). MSC: 65K05 65F30 15A24 PDFBibTeX XMLCite \textit{D. F. Shanno}, Math. Comput. 34, 499--514 (1980; Zbl 0424.65027) Full Text: DOI
Lichnewsky, A. Une méthode de gradient conjugue sur des variétés. Application à certains problèmes de valeurs propres non linéaires. (French) Zbl 0455.49020 Numer. Funct. Anal. Optimization 1, 515-560 (1979). MSC: 90C52 47J10 58E15 PDFBibTeX XMLCite \textit{A. Lichnewsky}, Numer. Funct. Anal. Optim. 1, 515--560 (1979; Zbl 0455.49020) Full Text: DOI