Pestana, Jennifer; Rees, Tyrone Null-space preconditioners for saddle point systems. (English) Zbl 1347.65060 SIAM J. Matrix Anal. Appl. 37, No. 3, 1103-1128 (2016). MSC: 65F08 65F10 65F50 PDF BibTeX XML Cite \textit{J. Pestana} and \textit{T. Rees}, SIAM J. Matrix Anal. Appl. 37, No. 3, 1103--1128 (2016; Zbl 1347.65060) Full Text: DOI OpenURL
Ansari, Mohammad Reza; Mahdavi-Amiri, Nezam A robust combined trust region-line search exact penalty projected structured scheme for constrained nonlinear least squares. (English) Zbl 1326.49048 Optim. Methods Softw. 30, No. 1, 162-190 (2015). Reviewer: Bülent Karasözen (Ankara) MSC: 49M37 90C53 90C55 PDF BibTeX XML Cite \textit{M. R. Ansari} and \textit{N. Mahdavi-Amiri}, Optim. Methods Softw. 30, No. 1, 162--190 (2015; Zbl 1326.49048) Full Text: DOI OpenURL
Cai, Li; Wang, Zhujun; Zhu, Detong A line search filter inexact reduced Hessian method for nonlinear equality constrained optimization. (English) Zbl 1317.49043 J. Appl. Math. Comput. 48, No. 1-2, 365-380 (2015). MSC: 49M37 90C30 65K05 PDF BibTeX XML Cite \textit{L. Cai} et al., J. Appl. Math. Comput. 48, No. 1--2, 365--380 (2015; Zbl 1317.49043) Full Text: DOI OpenURL
Mahdavi-Amiri, Nezam; Ansari, Mohammad Reza A superlinearly convergent exact penalty method for constrained nonlinear least squares: global analysis. (English) Zbl 1279.65077 Optimization 62, No. 6, 675-691 (2013). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C30 90C52 90C53 90C55 93E24 PDF BibTeX XML Cite \textit{N. Mahdavi-Amiri} and \textit{M. R. Ansari}, Optimization 62, No. 6, 675--691 (2013; Zbl 1279.65077) Full Text: DOI OpenURL
Liu, Tao-Wen A reduced Hessian SQP method for inequality constrained optimization. (English) Zbl 1242.90298 Comput. Optim. Appl. 49, No. 1, 31-59 (2011). MSC: 90C55 90C30 PDF BibTeX XML Cite \textit{T.-W. Liu}, Comput. Optim. Appl. 49, No. 1, 31--59 (2011; Zbl 1242.90298) Full Text: DOI OpenURL
Gu, Chao; Zhu, Detong A secant algorithm with line search filter method for nonlinear optimization. (English) Zbl 1205.90007 Appl. Math. Modelling 35, No. 2, 879-894 (2011). MSC: 90-04 90C30 PDF BibTeX XML Cite \textit{C. Gu} and \textit{D. Zhu}, Appl. Math. Modelling 35, No. 2, 879--894 (2011; Zbl 1205.90007) Full Text: DOI OpenURL
Liu, Tao-Wen; Li, Dong-Hui A cautious BFGS update for reduced Hessian SQP. (English) Zbl 1117.65090 Numer. Algorithms 44, No. 1, 11-28 (2007). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 65K05 90C30 90C53 90C06 PDF BibTeX XML Cite \textit{T.-W. Liu} and \textit{D.-H. Li}, Numer. Algorithms 44, No. 1, 11--28 (2007; Zbl 1117.65090) Full Text: DOI OpenURL
Zhu, Detong An affine scaling projective reduced Hessian algorithm for minimum optimization with nonlinear equality and linear inequality constraints. (English) Zbl 1078.65057 Appl. Math. Comput. 166, No. 1, 131-163 (2005). Reviewer: Karel Zimmermann (Praha) MSC: 65K05 90C30 90C26 90C51 PDF BibTeX XML Cite \textit{D. Zhu}, Appl. Math. Comput. 166, No. 1, 131--163 (2005; Zbl 1078.65057) Full Text: DOI OpenURL
Zhu, Detong An interior affine scaling projective algorithm for nonlinear equality and linear inequality constrained optimization. (English) Zbl 1070.65045 J. Comput. Appl. Math. 173, No. 1, 115-148 (2005). Reviewer: H. Ratschek (Düsseldorf) MSC: 65K05 90C30 90C51 PDF BibTeX XML Cite \textit{D. Zhu}, J. Comput. Appl. Math. 173, No. 1, 115--148 (2005; Zbl 1070.65045) Full Text: DOI OpenURL
Zhu, Detong A two-piece update of projected Hessian algorithm with nonmonotonic trust region method for constrained optimization. (English) Zbl 1071.65091 Appl. Math. Comput. 157, No. 1, 127-151 (2004). Reviewer: Dorel I. Duca (Cluj-Napoca) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{D. Zhu}, Appl. Math. Comput. 157, No. 1, 127--151 (2004; Zbl 1071.65091) Full Text: DOI OpenURL
Zhu, Detong Secant algorithms with nonmonotone trust region that employs Fletcher penalty function for constrained optimization. (English) Zbl 1049.90093 Optimization 50, No. 1-2, 121-153 (2001). MSC: 90C30 65K10 PDF BibTeX XML Cite \textit{D. Zhu}, Optimization 50, No. 1--2, 121--153 (2001; Zbl 1049.90093) Full Text: DOI OpenURL
Zhu, Detong A family of improved secant methods via nonmonotone curvilinear paths technique for equality constrained optimization. (English) Zbl 0989.65064 J. Comput. Appl. Math. 136, No. 1-2, 73-97 (2001). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C30 90C55 PDF BibTeX XML Cite \textit{D. Zhu}, J. Comput. Appl. Math. 136, No. 1--2, 73--97 (2001; Zbl 0989.65064) Full Text: DOI OpenURL
Zhu, Detong Nonmonotonic projected algorithm with both trust region and line search for constrained optimization. (English) Zbl 0951.65056 J. Comput. Appl. Math. 117, No. 1, 35-60 (2000). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{D. Zhu}, J. Comput. Appl. Math. 117, No. 1, 35--60 (2000; Zbl 0951.65056) Full Text: DOI OpenURL
Yu, Wenhuan A quasi-Newton method for estimating the parameter in a nonlinear hyperbolic system. (English) Zbl 1040.90049 J. Math. Anal. Appl. 231, No. 2, 397-424 (1999). MSC: 90C53 47J25 49M30 65M32 PDF BibTeX XML Cite \textit{W. Yu}, J. Math. Anal. Appl. 231, No. 2, 397--424 (1999; Zbl 1040.90049) Full Text: DOI OpenURL
Spellucci, P. An SQP method for general nonlinear programs using only equality constrained subproblems. (English) Zbl 0930.90082 Math. Program. 82, No. 3 (A), 413-448 (1998). MSC: 90C55 90C30 PDF BibTeX XML Cite \textit{P. Spellucci}, Math. Program. 82, No. 3 (A), 413--448 (1998; Zbl 0930.90082) Full Text: DOI OpenURL
Rheinboldt, W. C. Geometric notes on optimization with equality constraints. (English) Zbl 0852.90119 Appl. Math. Lett. 9, No. 3, 83-87 (1996). MSC: 90C30 PDF BibTeX XML Cite \textit{W. C. Rheinboldt}, Appl. Math. Lett. 9, No. 3, 83--87 (1996; Zbl 0852.90119) Full Text: DOI OpenURL
Rustem, B. Two-step and three-step Q-superlinear convergence of SQP methods. (English) Zbl 0813.90105 J. Optimization Theory Appl. 83, No. 3, 613-619 (1994). MSC: 90C30 PDF BibTeX XML Cite \textit{B. Rustem}, J. Optim. Theory Appl. 83, No. 3, 613--619 (1994; Zbl 0813.90105) Full Text: DOI OpenURL
Zhang, Jianzhong; Zhu, Detong A convergent secant method for constrained optimization. (English) Zbl 0809.65061 Japan J. Ind. Appl. Math. 11, No. 2, 265-288 (1994). Reviewer: J.Terno (Dresden) MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{J. Zhang} and \textit{D. Zhu}, Japan J. Ind. Appl. Math. 11, No. 2, 265--288 (1994; Zbl 0809.65061) Full Text: DOI OpenURL
Huschens, J. Exploiting additional structure in equality constrained optimization by structured SQP secant algorithms. (English) Zbl 0792.90069 J. Optimization Theory Appl. 77, No. 2, 343-358 (1993). MSC: 90C30 PDF BibTeX XML Cite \textit{J. Huschens}, J. Optim. Theory Appl. 77, No. 2, 343--358 (1993; Zbl 0792.90069) Full Text: DOI OpenURL
Rustem, B. Equality and inequality constrained optimization algorithms with convergent stepsizes. (English) Zbl 0797.90097 J. Optimization Theory Appl. 76, No. 3, 429-453 (1993). MSC: 90C30 90-08 PDF BibTeX XML Cite \textit{B. Rustem}, J. Optim. Theory Appl. 76, No. 3, 429--453 (1993; Zbl 0797.90097) Full Text: DOI OpenURL
Bartholomew-Biggs, M. C.; Nguyen, T. T. Orthogonal and conjugate basis methods for solving equality constrained minimization problems. (English) Zbl 0790.65052 Comput. Optim. Appl. 2, No. 2, 171-200 (1993). Reviewer: S.Zabek (Lublin) MSC: 65K05 90C30 90C20 90-08 PDF BibTeX XML Cite \textit{M. C. Bartholomew-Biggs} and \textit{T. T. Nguyen}, Comput. Optim. Appl. 2, No. 2, 171--200 (1993; Zbl 0790.65052) Full Text: DOI OpenURL
Liao, Aiping A reduced Hessian method for constrained optimization. (English) Zbl 0794.90065 Comput. Optim. Appl. 2, No. 2, 129-143 (1993). MSC: 90C30 PDF BibTeX XML Cite \textit{A. Liao}, Comput. Optim. Appl. 2, No. 2, 129--143 (1993; Zbl 0794.90065) Full Text: DOI OpenURL
Coleman, Thomas F.; Liao, Ai-Ping The local convergence of the Byrd-Schnabel algorithm for constrained optimization. (English) Zbl 0773.90066 Appl. Math. Lett. 6, No. 3, 37-42 (1993). MSC: 90C30 65K05 90-08 PDF BibTeX XML Cite \textit{T. F. Coleman} and \textit{A.-P. Liao}, Appl. Math. Lett. 6, No. 3, 37--42 (1993; Zbl 0773.90066) Full Text: DOI OpenURL
Zhang, Yin Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization. (English) Zbl 0773.90056 Math. Program. 55, No. 1 (A), 109-124 (1992). MSC: 90C25 90-08 PDF BibTeX XML Cite \textit{Y. Zhang}, Math. Program. 55, No. 1 (A), 109--124 (1992; Zbl 0773.90056) Full Text: DOI OpenURL
Coleman, Thomas F.; Fenyes, Peter A. Partitioned quasi-Newton methods for nonlinear equality constrained optimization. (English) Zbl 0751.90070 Math. Program., Ser. A 53, No. 1, 17-44 (1992). Reviewer: Wang Zeke (Guangzhou) MSC: 90C30 65K05 90-08 49M30 65H10 90C20 65K10 PDF BibTeX XML Cite \textit{T. F. Coleman} and \textit{P. A. Fenyes}, Math. Program. 53, No. 1 (A), 17--44 (1992; Zbl 0751.90070) Full Text: DOI OpenURL
Kupfer, F.-S.; Sachs, E. W. Numerical solution of a nonlinear parabolic control problem by a reduced SQP method. (English) Zbl 0771.49010 Comput. Optim. Appl. 1, No. 1, 113-135 (1992). Reviewer: W.H.Schmidt (Greifswald) MSC: 90C20 49J20 35K05 90C90 90-08 49N70 49N75 PDF BibTeX XML Cite \textit{F. S. Kupfer} and \textit{E. W. Sachs}, Comput. Optim. Appl. 1, No. 1, 113--135 (1992; Zbl 0771.49010) Full Text: DOI OpenURL
Gilbert, Jean Charles Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization. (English) Zbl 0721.90068 Math. Program., Ser. A 50, No. 1, 1-28 (1991). Reviewer: C.Vârsan (Bucureşti) MSC: 90C30 49M30 90-08 PDF BibTeX XML Cite \textit{J. C. Gilbert}, Math. Program. 50, No. 1 (A), 1--28 (1991; Zbl 0721.90068) 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
Zhang, Jianzhong; Zhu, Detong; Hou, Shaoping Some improved projected quasi-Newton algorithms and their convergence. II: Local convergence rate and numerical tests. (English) Zbl 0683.65047 Acta Math. Appl. Sin., Engl. Ser. 5, No. 1, 46-59 (1989). Reviewer: H.Benker MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{J. Zhang} et al., Acta Math. Appl. Sin., Engl. Ser. 5, No. 1, 46--59 (1989; Zbl 0683.65047) Full Text: DOI OpenURL
Gilbert, J. Ch. On the local and global convergence of a reduced quasi-Newton method. (English) Zbl 0676.90061 Optimization 20, No. 4, 421-450 (1989). MSC: 90C30 65K05 49M30 49M05 PDF BibTeX XML Cite \textit{J. Ch. Gilbert}, Optimization 20, No. 4, 421--450 (1989; Zbl 0676.90061) Full Text: DOI OpenURL
Tapia, Richard On secant updates for use in general constrained optimization. (English) Zbl 0657.90088 Math. Comput. 51, No. 183, 181-202 (1988). Reviewer: S.Mititelu MSC: 90C30 65K05 90C20 49M15 PDF BibTeX XML Cite \textit{R. Tapia}, Math. Comput. 51, No. 183, 181--202 (1988; Zbl 0657.90088) 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
Fontecilla, R. A heuristic algorithm for nonlinear programming. (English) Zbl 0628.90061 J. Optimization Theory Appl. 58, No. 3, 431-442 (1988). MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{R. Fontecilla}, J. Optim. Theory Appl. 58, No. 3, 431--442 (1988; Zbl 0628.90061) Full Text: DOI OpenURL
Byrd, Richard H.; Schnabel, Robert B. Continuity of the null space basis and constrained optimization. (English) Zbl 0598.90072 Math. Program. 35, 32-41 (1986). Reviewer: M.Rijckaert MSC: 90C30 49M37 PDF BibTeX XML Cite \textit{R. H. Byrd} and \textit{R. B. Schnabel}, Math. Program. 35, 32--41 (1986; Zbl 0598.90072) Full Text: DOI OpenURL
Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Stewart, G. W.; Wright, Margaret H. Properties of a representation of a basis for the null space. (English) Zbl 0579.65035 Math. Program. 33, 172-186 (1985). Reviewer: K.Schittkowski MSC: 65F30 90C30 65K05 15A23 PDF BibTeX XML Cite \textit{P. E. Gill} et al., Math. Program. 33, 172--186 (1985; Zbl 0579.65035) Full Text: DOI OpenURL