{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,13]],"date-time":"2025-07-13T03:40:09Z","timestamp":1752378009223,"version":"3.41.2"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational Optimization and Applications"],"published-print":{"date-parts":[[2000,7]]},"DOI":"10.1023\/a:1008701324575","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T11:37:32Z","timestamp":1040557052000},"page":"121-158","source":"Crossref","is-referenced-by-count":2,"title":["A Piecewise Line-Search Technique for Maintaining the Positive Definitenes of the Matrices in the SQP Method"],"prefix":"10.1007","volume":"16","author":[{"given":"Paul","family":"Armand","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. Charles","family":"Gilbert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"265231_CR1","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1137\/0805017","volume":"5","author":"L.T. Biegler","year":"1995","unstructured":"L.T. Biegler, J. Nocedal, and C. Schmid, \u201cAreduced Hessian method for large-scale constrained optimization,\u201d SIAM Journal on Optimization,\u201d vol. 5, pp. 314\u2013347, 1995.","journal-title":"SIAM Journal on Optimization"},{"key":"265231_CR2","doi-asserted-by":"crossref","unstructured":"P.T. Boggs and J.W. Tolle, \u201cSequential quadratic programming,\u201d in Acta Numerica 1995, Cambridge University Press, pp. 1-51, 1995.","DOI":"10.1017\/S0962492900002518"},{"key":"265231_CR3","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0327033","volume":"27","author":"J.F. Bonnans","year":"1989","unstructured":"J.F. Bonnans, \u201cAsymptotic admissibility of the unit stepsize in exact penalty methods,\u201d SIAM Journal on Control and Optimization, vol. 27, pp. 631\u2013641, 1989.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"265231_CR4","volume-title":"Math\u00e9matiques et Applications, vol. 27: Optimisation Num\u00e9rique-Aspects th\u00e9oriques et pratiques","author":"J.F. Bonnans","year":"1997","unstructured":"J.F. Bonnans, J.Ch. Gilbert, C. Lemar\u00e9chal, and C. Sagastiz\u00e1bal, Math\u00e9matiques et Applications, vol. 27: Optimisation Num\u00e9rique-Aspects th\u00e9oriques et pratiques, Springer Verlag: Berlin, 1997."},{"key":"265231_CR5","unstructured":"R.H. Byrd, J.Ch. Gilbert, and J. Nocedal, \u201cA trust region method based on interior point techniques for nonlinear programming,\u201d Rapport de Recherche 2896, INRIA, 1996. (Submitted to Mathematical Programming)"},{"key":"265231_CR6","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1137\/0726042","volume":"26","author":"R.H. Byrd","year":"1989","unstructured":"R.H. Byrd and J. Nocedal, \u201cA tool for the analysis of quasi-Newton methods with application to unconstrained minimization,\u201d SIAM Journal on Numerical Analysis, vol. 26, pp. 727\u2013739, 1989.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"265231_CR7","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF01588794","volume":"49","author":"R.H. Byrd","year":"1991","unstructured":"R.H. Byrd and J. Nocedal, \u201cAn analysis of reduced Hessian methods for constrained optimization,\u201d Mathematical Programming, vol. 49, pp. 285\u2013323, 1991.","journal-title":"Mathematical Programming"},{"key":"265231_CR8","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1137\/0802012","volume":"2","author":"R.H. Byrd","year":"1992","unstructured":"R.H. Byrd, R.A. Tapia, and Y. Zhang, \u201cAn SQP augmented Lagrangian BFGS algorithm for constrained optimization,\u201d SIAM Journal on Optimization, vol. 2, pp. 210\u2013241, 1992.","journal-title":"SIAM Journal on Optimization"},{"key":"265231_CR9","volume-title":"Optimization and Nonsmooth Analysis","author":"F.H. Clarke","year":"1983","unstructured":"F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons: New York, 1983."},{"key":"265231_CR10","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1137\/0721051","volume":"21","author":"T.F. Coleman","year":"1984","unstructured":"T.F. Coleman and A.R. Conn, \u201cOn the local convergence of a quasi-Newton method for the nonlinear programming problem,\u201d SIAM Journal on Numerical Analysis, vol. 21, pp. 755\u2013769, 1984.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"265231_CR11","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/BF01585692","volume":"53","author":"T.F. Coleman","year":"1992","unstructured":"T.F. Coleman and P.A. Fenyes, \u201cPartitioned quasi-Newton methods for nonlinear constrained optimization,\u201d Mathematical Programming, vol. 53, pp. 17\u201344, 1992.","journal-title":"Mathematical Programming"},{"key":"265231_CR12","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"J.E. Dennis","year":"1983","unstructured":"J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall: Englewood Cliffs, 1983."},{"key":"265231_CR13","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1137\/0730067","volume":"30","author":"J.E. Dennis","year":"1993","unstructured":"J.E. Dennis and H. Wolkowicz, \u201cSizing and least-change secant methods,\u201d SIAM Journal on Numerical Analysis, vol. 30, pp. 1291\u20131314, 1993.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"265231_CR14","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"1987","unstructured":"R. Fletcher, Practical Methods of Optimization, 2nd ed., John Wiley & Sons: Chichester, 1987.","edition":"2nd ed."},{"key":"265231_CR15","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF00934767","volume":"37","author":"D. Gabay","year":"1982","unstructured":"D. Gabay, \u201cMinimizing a differentiable function over a differential manifold,\u201d Journal of Optimization Theory and Applications, vol. 37, pp. 177\u2013219, 1982.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"265231_CR16","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/BFb0120946","volume":"16","author":"D. Gabay","year":"1982","unstructured":"D. Gabay, \u201cReduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization,\u201d Mathematical Programming Study, vol. 16, pp. 18\u201344, 1982.","journal-title":"Mathematical Programming Study"},{"key":"265231_CR17","first-page":"251","volume":"22","author":"J. Gilbert","year":"1988","unstructured":"J.Ch. Gilbert, \u201cMise \u00e0 jour de la m\u00e9trique dans les m\u00e9thodes de quasi-Newton r\u00e9duites en optimisation avec contraintes d'\u00e9galit\u00e9,\u201d Mod\u00e9lisation Math\u00e9matique et Analyse Num\u00e9rique, vol. 22, pp. 251\u2013288, 1988.","journal-title":"Mod\u00e9lisation Math\u00e9matique et Analyse Num\u00e9rique"},{"key":"265231_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01594922","volume":"50","author":"J. Gilbert","year":"1991","unstructured":"J.Ch. Gilbert, \u201cMaintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization,\u201d Mathematical Programming, vol. 50, pp. 1\u201328, 1991.","journal-title":"Mathematical Programming"},{"key":"265231_CR19","unstructured":"J.Ch. Gilbert, \u201cSuperlinear convergence of a reduced BFGS method with piecewise line-search and update criterion,\u201d Rapport de Recherche 2140, INRIA, BP 105, 78153 Le Chesnay, France, 1993. http:\/\/www.inria.fr\/RRRT\/RR-2140.html; ftp:\/\/ftp.inria.fr\/INRIA\/publication\/RR, RR-2140.ps.gz."},{"key":"265231_CR20","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1137\/S1052623493259604","volume":"7","author":"J. Gilbert","year":"1997","unstructured":"J.Ch. Gilbert, \u201cOn the realization of the Wolfe conditions in reduced quasi-Newton methods for equality constrained optimization,\u201d SIAM Journal on Optimization, vol. 7, pp. 780\u2013813, 1997.","journal-title":"SIAM Journal on Optimization"},{"key":"265231_CR21","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1137\/0804026","volume":"4","author":"C.B. Gurwitz","year":"1994","unstructured":"C.B. Gurwitz, \u201cLocal convergence of a two-piece update of a projected Hessian matrix,\u201d SIAM Journal on Optimization, vol. 4, pp. 461\u2013485, 1994.","journal-title":"SIAM Journal on Optimization"},{"key":"265231_CR22","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01580395","volume":"11","author":"S.-P. Han","year":"1976","unstructured":"S.-P. Han, \u201cSuperlinearly convergent variable metric algorithms for general nonlinear programming problems,\u201d Mathematical Programming, vol. 11, pp. 263\u2013282, 1976.","journal-title":"Mathematical Programming"},{"key":"265231_CR23","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/BF01588250","volume":"17","author":"S.-P. Han","year":"1979","unstructured":"S.-P. Han and O.L. Mangasarian, \u201cExact penalty functions in nonlinear programming,\u201d Mathematical Programming, vol. 17, pp. 251\u2013269, 1979.","journal-title":"Mathematical Programming"},{"key":"265231_CR24","doi-asserted-by":"crossref","unstructured":"J.-B. Hiriart-Urruty and C. Lemar\u00e9chal, Convex Analysis and Minimization Algorithms, Springer-Verlag, 1993, Grundlehren der mathematischen Wissenschaften 305-306.","DOI":"10.1007\/978-3-662-02796-7"},{"key":"265231_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-48320-2","volume-title":"Lecture Notes in Economics and Mathematical Systems, vol. 187: Test Examples for Nonlinear Programming Codes","author":"W. Hock","year":"1981","unstructured":"W. Hock and K. Schittkowski, Lecture Notes in Economics and Mathematical Systems, vol. 187: Test Examples for Nonlinear Programming Codes, Springer-Verlag: Berlin, 1981."},{"key":"265231_CR26","volume-title":"Nonlinear Programming","author":"O.L. Mangasarian","year":"1969","unstructured":"O.L. Mangasarian, Nonlinear Programming, McGraw-Hill: New York, 1969."},{"key":"265231_CR27","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1137\/0722050","volume":"22","author":"J. Nocedal","year":"1985","unstructured":"J. Nocedal and M.L. Overton, \u201cProjected Hessian updating algorithms for nonlinearly constrained optimization,\u201d SIAM Journal on Numerical Analysis, vol. 22, pp. 821\u2013850, 1985.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"265231_CR28","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1093\/comjnl\/12.2.171","volume":"12","author":"J.D. Pearson","year":"1969","unstructured":"J.D. Pearson, \u201cVariable metric methods of minimization,\u201d The Computer Journal, vol. 12, pp. 171\u2013178, 1969.","journal-title":"The Computer Journal"},{"key":"265231_CR29","first-page":"27","volume-title":"Nonlinear Programming, vol. 3","author":"M.J.D. Powell","year":"1978","unstructured":"M.J.D. Powell, \u201cThe convergence of variable metric methods for nonlinearly constrained optimization calculations,\u201d in Nonlinear Programming, vol. 3, O.L. Mangasarian, R.R. Meyer, and S.M. Robinson (Eds.), Academic Press: New York, 1978, pp. 27\u201363."},{"key":"265231_CR30","first-page":"144","volume-title":"Lecture Notes in Mathematics, vol. 630: Numerical Analysis Dundee 1977","author":"M.J.D. Powell","year":"1978","unstructured":"M.J.D. Powell, \u201cA fast algorithm for nonlinearly constrained optimization calculations,\u201d in Lecture Notes in Mathematics, vol. 630: Numerical Analysis Dundee 1977, G.A.Watson (Ed.), Springer-Verlag: Berlin, 1978, pp. 144\u2013157."},{"key":"265231_CR31","first-page":"160","volume-title":"Numerical Optimization 1984","author":"M.J.D. Powell","year":"1985","unstructured":"M.J.D. Powell, \u201cThe performance of two subroutines for constrained optimization on some difficult test problems,\u201d in Numerical Optimization 1984, P.T. Boggs, R.H. Byrd, and R.B. Schnabel (Eds.), SIAM Publication: Philadelphia, 1985, pp. 160\u2013177."},{"key":"265231_CR32","first-page":"119","volume-title":"History of Mathematical Programming, A Collection of Personal Reminiscences","author":"M.J.D. Powell","year":"1991","unstructured":"M.J.D. Powell, \u201cA view of nonlinear optimization,\u201d in History of Mathematical Programming, A Collection of Personal Reminiscences, J.K. Lenstra, A.H.G. Rinnooy Kan, and A. Schrijver (Eds.), CWI North-Holland: Amsterdam, 1991, pp. 119\u2013125."},{"key":"265231_CR33","doi-asserted-by":"crossref","unstructured":"K. Schittkowski, Lecture Notes in Economics and Mathematical Systems, vol. 282: More Test Examples for Nonlinear Programming Codes, Springer-Verlag, 1987.","DOI":"10.1007\/978-3-642-61582-5"},{"key":"265231_CR34","volume-title":"Analyse II-Calcul Diff\u00e9rentiel et \u00c9quations Diff\u00e9rentielles","author":"L. Schwartz","year":"1992","unstructured":"L. Schwartz, Analyse II-Calcul Diff\u00e9rentiel et \u00c9quations Diff\u00e9rentielles, Hermann, Paris, 1992."},{"key":"265231_CR35","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF00933161","volume":"22","author":"R.A. Tapia","year":"1977","unstructured":"R.A. Tapia, \u201cDiagonalized multiplier methods and quasi-Newton methods for constrained optimization,\u201d Journal of Optimization Theory and Applications, vol. 22, pp. 135\u2013194, 1977.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"265231_CR36","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1090\/S0025-5718-1988-0942149-3","volume":"51","author":"R.A. Tapia","year":"1988","unstructured":"R.A. Tapia, \u201cOn secant updates for use in general constrained optimization,\u201d Mathematics of Computation, vol. 51, pp. 181\u2013202, 1988.","journal-title":"Mathematics of Computation"},{"key":"265231_CR37","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1137\/1011036","volume":"11","author":"P. Wolfe","year":"1969","unstructured":"P. Wolfe, \u201cConvergence conditions for ascent methods,\u201d SIAM Review, vol. 11, pp. 226\u2013235, 1969.","journal-title":"SIAM Review"},{"key":"265231_CR38","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1137\/1013035","volume":"13","author":"P. Wolfe","year":"1971","unstructured":"P.Wolfe, \u201cConvergence conditions for ascent methods II: Some corrections,\u201d SIAM Review, vol. 13, pp. 185\u2013188, 1971.","journal-title":"SIAM Review"},{"key":"265231_CR39","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1137\/S105262349427861X","volume":"9","author":"Y. Xie","year":"1999","unstructured":"Y. Xie and R.H. Byrd \u201cPractical update criteria for reduced Hessian SQP: global analysis,\u201d SIAM Journal on Optimization, vol. 9, pp. 578\u2013604, 1999.","journal-title":"SIAM Journal on Optimization"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008701324575.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1008701324575\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008701324575.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,13]],"date-time":"2025-07-13T03:27:05Z","timestamp":1752377225000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1008701324575"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,7]]}},"alternative-id":["265231"],"URL":"https:\/\/doi.org\/10.1023\/a:1008701324575","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2000,7]]}}}