{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T01:14:38Z","timestamp":1787706878584,"version":"build-2784847793"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,11]]},"abstract":"<jats:p>The aim of this paper is to define a new class of minimization algorithms for solving large scale unconstrained problems. In particular we describe a stabilization framework, based on a curvilinear linesearch, which uses a combination of a Newton-type direction and a negative curvature direction. The motivation for using negative curvature direction is that of taking into account local nonconvexity of the objective function. On the basis of this framework, we propose an algorithm which uses the Lanczos method for determining at each iteration both a Newton-type direction and an effective negative curvature direction. The results of extensive numerical testing are reported together with a comparison with the LANCELOT package. These results show that the algorithm is very competitive, which seems to indicate that the proposed approach is promising.<\/jats:p>","DOI":"10.1137\/s1052623495295250","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"916-939","source":"Crossref","is-referenced-by-count":49,"title":["Curvilinear Stabilization Techniques for Truncated Newton Methods in Large Scale Unconstrained Optimization"],"prefix":"10.1137","volume":"8","author":[{"given":"Stefano","family":"Lucidi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Rochetich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Massimo","family":"Roma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"M. Arioli, T. Chan, I. Duff, N. Gould, and J. K. Reid,\n                      Computing a Search Direction for Large\u2010Scale Linearly\u2010Constrained Nonlinear Optimization Calculations\n                      , Technical report TR\/PA\/93\/34, CERFACS, 1993."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1145\/200979.201043"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Conn, N. Gould, and P. Toint,\n                      LANCELOT: A Fortran Package for Large\u2010Scale Nonlinear Optimization (Release A)\n                      , Springer\u2010Verlag, Heidelberg, Berlin, 1992.","DOI":"10.1007\/978-3-662-12211-2"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"J. Cullum and R. Willoughby,\n                      Lanczos Algorithms for Large Symmetric Eigenvalue Computations\n                      , Birkhauser, Boston, 1985.","DOI":"10.1007\/978-1-4684-9190-6"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0719025"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592055"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00939608"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249642"},{"key":"R9","volume-title":"Practical methods of optimization","author":"Fletcher R.","year":"1987"},{"key":"R10","unstructured":"G. Golub and C. Van Loan,\n                      Matrix Computations\n                      , 2nd ed., The John Hopkins Press, Baltimore, 1989."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0723046"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940345"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385810"},{"key":"R14","unstructured":"S. Lucidi, F. Rochetich, and M. Roma,\n                      Curvilinear Stabilization Techniques for Truncated Newton Methods in Large Scale Unconstrained Optimization: The Complete Results\n                      , Technical report 02.95, Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Roma \u201c\u201da Sapienza,\" 1995."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584328"},{"key":"R16","volume-title":"Nonlinear programming","author":"McCormick Garth","year":"1983"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582091"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/0721052"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0906042"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719468"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/0712047"},{"key":"R22","unstructured":"B. Parlett,\n                      The Symmetric Eigenvalue Problem\n                      , Prentice\u2010Hall Series in Computational Mathematics, Prentice\u2010Hall, Englewood Cliffs, NJ, 1980."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1145\/128745.150973"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/0722003"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0613025"},{"key":"R26","unstructured":"P. Toint,\n                      Towards an efficient sparsity exploiting Newton method for minimization\n                      , in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57\u201388."},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759427021X"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(96)00065-2"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238640"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623495295250","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:54:38Z","timestamp":1787331278000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623495295250"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["10.1137\/S1052623495295250"],"URL":"https:\/\/doi.org\/10.1137\/s1052623495295250","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,11]]}}}