{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:16:28Z","timestamp":1768738588456,"version":"3.49.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1988,4,1]],"date-time":"1988-04-01T00:00:00Z","timestamp":575856000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1988,4]]},"DOI":"10.1007\/bf01589407","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T09:09:36Z","timestamp":1114679376000},"page":"273-306","source":"Crossref","is-referenced-by-count":48,"title":["Parallel quasi-Newton methods for unconstrained optimization"],"prefix":"10.1007","volume":"42","author":[{"given":"Richard H.","family":"Byrd","sequence":"first","affiliation":[]},{"given":"Robert B.","family":"Schnabel","sequence":"additional","affiliation":[]},{"given":"Gerald A.","family":"Shultz","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1093\/imamat\/11.1.73","volume":"11","author":"K.W. Brodlie","year":"1973","unstructured":"K.W. Brodlie, A.R. Gourlay and J. Greenstadt, \u201cRank-one and rank-two corrections to positive definite matrices expressed in product form,\u201dJournal of the Institute of Mathematics and its Applications 11 (1973) 73\u201382.","journal-title":"Journal of the Institute of Mathematics and its Applications"},{"key":"CR2","unstructured":"R.H. Byrd and J. Nocedal, \u201cA tool for the analysis of quasi-Newton methods with application to unconstrained minimization,\u201d Technical Report ANL\/MCS-TM-103, Mathematics and Computer Science Division, Argonne National Laboratory (1987)."},{"key":"CR3","unstructured":"R.H. Byrd, R.B. Schnabel and G.A. Shultz, \u201cUsing parallel function evaluations to improve Hessian approximations for unconstrained optimization,\u201d Technical Report CU-CS-361\u201387, Department of Computer Science, University of Colorado at Boulder (1987), to appear inAnnals of Operations Research."},{"key":"CR4","volume-title":"\u201cTesting a class of methods for solving minimization problems with simple bounds on the variables,\u201d Research Report CS-86\u201345","author":"A.R. Conn","year":"1986","unstructured":"A.R. Conn, N.I.M. Gould and Ph.L. Toint, \u201cTesting a class of methods for solving minimization problems with simple bounds on the variables,\u201d Research Report CS-86\u201345, Faculty of Mathematics, University of Waterloo, Waterloo, Canada (1986)."},{"key":"CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01681328","volume":"9","author":"W.C. Davidon","year":"1975","unstructured":"W.C. Davidon, \u201cOptimally conditioned optimization algorithms without line searches,\u201dMathematical Programming 9 (1975) 1\u201330.","journal-title":"Mathematical Programming"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1090\/S0025-5718-1974-0343581-1","volume":"28","author":"J.E. Dennis Jr.","year":"1974","unstructured":"J.E. Dennis Jr. and J.J. Mor\u00e9, \u201cA characterization of superlinear convergence and its application to quasi-Newton methods,\u201dMathematics of Computation 28 (1974) 549\u2013560.","journal-title":"Mathematics of Computation"},{"key":"CR7","volume-title":"Numerical Methods for Nonlinear Equations and Unconstrained Optimization","author":"J.E. Dennis Jr.","year":"1983","unstructured":"J.E. Dennis Jr. and R.B. Schnabel,Numerical Methods for Nonlinear Equations and Unconstrained Optimization (Prentice-Hall, Englewood Cliffs, New Jersey, 1983)."},{"key":"CR8","volume-title":"Handbooks in Operations Research and Management Science, Vol. 1,Optimization","author":"J.E. Dennis Jr.","year":"1987","unstructured":"J.E. Dennis Jr. and R.B. Schnabel, \u201cA view of unconstrained optimization,\u201d Technical Report CU-CS-376-87, Department of Computer Science, University of Colorado at Boulder, to appear in: G.L. Nemhauser, A.H.J. Rinnoy Kan and M.J. Todd, eds.,Handbooks in Operations Research and Management Science, Vol. 1,Optimization (North-Holland, Amsterdam, 1987)."},{"key":"CR9","unstructured":"L.C.W. Dixon, \u201cThe place of parallel computation in numerical optimisation I, the local problem,\u201d Technical Report No. 118, Numerical Optimisation Centre, The Hatfield Polytechnic (1981)."},{"key":"CR10","unstructured":"L.C.W. Dixon and K.D. Patel, \u201cThe place of parallel computation in numerical optimisation IV, parallel algorithms for nonlinear optimisation,\u201d Technical Report No. 125, Numerical Optimisation Centre, The Hatfield Polytechnic (1982)."},{"key":"CR11","volume-title":"Practical Method of Optimization, Vol. 1, Unconstrained Optimization","author":"R. Fletcher","year":"1980","unstructured":"R. Fletcher,Practical Method of Optimization, Vol. 1, Unconstrained Optimization (John Wiley and Sons, New York, 1980)."},{"key":"CR12","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1090\/S0025-5718-1974-0343558-6","volume":"28","author":"P.E. Gill","year":"1974","unstructured":"P.E. Gill, G.H. Golub, W. Murray and N.A. Saunders, \u201cMethods for modifying matrix factorizations,\u201dMathematics of Computation 28 (1974) 505\u2013535.","journal-title":"Mathematics of Computation"},{"key":"CR13","volume-title":"Practical Optimization","author":"P.E. Gill","year":"1981","unstructured":"P.E. Gill, W. Murray and M.H. Wright,Practical Optimization (Academic Press, London, 1981)."},{"key":"CR14","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1090\/S0025-5718-1976-0423804-2","volume":"30","author":"D. Goldfarb","year":"1976","unstructured":"D. Goldfarb, \u201cFactorized variable metric methods for unconstrained optimization,\u201dMathematics of Computation 30 (1976) 796\u2013811.","journal-title":"Mathematics of Computation"},{"key":"CR15","unstructured":"L. Grandinetti, \u201cFactorization versus nonfactorization in quasi-Newtonian methods for differentiable optimization,\u201d Report N5, Dipartimento di Sistemi, Universita della Calabria (1978)."},{"key":"CR16","first-page":"82","volume-title":"Numerical Analysis: Pitman Research Notes in Mathematics Series 140","author":"S.P. Han","year":"1986","unstructured":"S.P. Han, \u201cOptimization by updated conjugate subspaces,\u201d in: D.F. Griffiths and G.A. Watson, eds.,Numerical Analysis: Pitman Research Notes in Mathematics Series 140 (Longman Scientific and Technical, Burnt Mill, England, 1986), pp. 82\u201397."},{"key":"CR17","unstructured":"F.A. Lootsma, \u201cParallel unconstrained optimization methods,\u201d Report No. 84\u201330, Department of Mathematics and Informatics, Technische Hogeschool Delft (1984)."},{"key":"CR18","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1145\/355934.355936","volume":"7","author":"J.J. Mor\u00e9","year":"1981","unstructured":"J.J. Mor\u00e9, B.S. Garbow and K.E. Hillstrom, \u201cTesting unconstrained optimization software,\u201dACM Transactions on Mathematical Software 7 (1981) 17\u201341.","journal-title":"ACM Transactions on Mathematical Software"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/0904038","volume":"4","author":"J.J. Mor\u00e9","year":"1983","unstructured":"J.J. Mor\u00e9 and D.C. Sorensen, \u201cComputing a trust region step,\u201dSIAM Journal on Scientific and Statistical Computing 4 (1983) 553\u2013572.","journal-title":"SIAM Journal on Scientific and Statistical Computing"},{"key":"CR20","doi-asserted-by":"crossref","unstructured":"B.A. Murtagh and M.A. Saunders, \u201cMINOS 5.0 User's Guide,\u201d Technical Report SOL 83\u201320, Department of Operations Research, Stanford University (1983).","DOI":"10.21236\/ADA138522"},{"key":"CR21","unstructured":"K.D. Patel, \u201cImplementation of a parallel (SIMD) modified Newton method on the ICL DAP,\u201d Technical Report No. 131, Numerical Optimisation Centre, The Hatfield Polytechnic (1982)."},{"key":"CR22","first-page":"53","volume-title":"Nonlinear Programming","author":"M.J.D. Powell","year":"1976","unstructured":"M.J.D. Powell, \u201cSome global convergence properties of a variable metric method without exact line searches,\u201d in: R. Cottle and C. Lemke, eds.,Nonlinear Programming (AMS, Providence, RI, 1976) pp. 53\u201372."},{"key":"CR23","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF02591850","volume":"38","author":"M.J.D. Powell","year":"1987","unstructured":"M.J.D. Powell, \u201cUpdating conjugate directions by the BFGS formula,\u201dMathematical Programming 38 (1987) 29\u201346.","journal-title":"Mathematical Programming"},{"key":"CR24","doi-asserted-by":"crossref","unstructured":"R.B. Schnabel, \u201cQuasi-Newton methods using multiple secant equations,\u201d Technical Report CU-CS-247\u201383, Department of Computer Science, University of Colorado at Boulder (1983).","DOI":"10.21236\/ADA131444"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/0045-7825(87)90055-7","volume":"64","author":"R.B. Schnabel","year":"1987","unstructured":"R.B. Schnabel, \u201cConcurrent function evaluations in local and global optimization,\u201dComputer Methods in Applied Mechanics and Engineering 64 (1987) 537\u2013552.","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"CR26","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1137\/0721054","volume":"21","author":"R.B. Schnabel","year":"1984","unstructured":"R.B. Schnabel and P. Frank, \u201cTensor methods for nonlinear equations,\u201dSIAM Journal on Numerical Analysis 21 (1984) 815\u2013843.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1145\/6187.6192","volume":"11","author":"R.B. Schnabel","year":"1985","unstructured":"R.B. Schnabel, J.E. Koontz and B.E. Weiss, \u201cA modular system of algorithms of unconstrained minimization,\u201dACM Transactions on Mathematical Software 11 (1985) 419\u2013440.","journal-title":"ACM Transactions on Mathematical Software"},{"key":"CR28","first-page":"145","volume":"14","author":"D.F. Shanno","year":"1987","unstructured":"D.F. Shanno and K.H. Phua, \u201cMatrix conditions and nonlinear optimization,\u201dMathematical Programming 14 (1987a) 145\u2013160.","journal-title":"Mathematical Programming"},{"key":"CR29","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/BF01582012","volume":"33","author":"P.J.M. Laarhoven van","year":"1985","unstructured":"P.J.M. van Laarhoven, \u201cParallel variable metric methods for unconstrained optimization,\u201dMathematical Programming 33 (1985) 68\u201381.","journal-title":"Mathematical Programming"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01589407.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01589407\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01589407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T03:52:29Z","timestamp":1586231549000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01589407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,4]]},"references-count":29,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1988,4]]}},"alternative-id":["BF01589407"],"URL":"https:\/\/doi.org\/10.1007\/bf01589407","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,4]]}}}