{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T18:41:15Z","timestamp":1649184075022},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1984,10,1]],"date-time":"1984-10-01T00:00:00Z","timestamp":465436800000},"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":[[1984,10]]},"DOI":"10.1007\/bf02591885","type":"journal-article","created":{"date-parts":[[2007,3,29]],"date-time":"2007-03-29T15:39:01Z","timestamp":1175182741000},"page":"196-217","source":"Crossref","is-referenced-by-count":3,"title":["Efficiency and implementation of simplicial zero point algorithms"],"prefix":"10.1007","volume":"30","author":[{"given":"G.","family":"van der Laan","sequence":"first","affiliation":[]},{"given":"L. P.","family":"Seelen","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02591885_CR1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1137\/1022003","volume":"22","author":"E.L. Allgower","year":"1980","unstructured":"E.L. Allgower and K. Georg, \u201cSimplicial and continuation methods for approximating fixed points and solutions to systems of equations\u201d,SIAM Review 22 (1980) 28\u201375.","journal-title":"SIAM Review"},{"key":"BF02591885_CR2","volume-title":"Computational experience with the octahedral algorithm and related results","author":"M.N. Broadie","year":"1983","unstructured":"M.N. Broadie, \u201cComputational experience with the octahedral algorithm and related results\u201d, Department of Operations Research, Stanford University (Stanford, California, 1983)."},{"key":"BF02591885_CR3","series-title":"Scientific Center Report 320-2949","volume-title":"A comparative study of nonlinear programming codes","author":"A.R. Colville","year":"1968","unstructured":"A.R. Colville, \u201cA comparative study of nonlinear programming codes, Scientific Center Report 320-2949, IBM (New York, 1968)."},{"key":"BF02591885_CR4","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1137\/1019005","volume":"19","author":"J.E. Dennis","year":"1977","unstructured":"J.E. Dennis and J.J. More, \u201cQuasi-Newton Methods, motivation and theory\u201d,SIAM Review 19 (1977), 46\u201389.","journal-title":"SIAM Review"},{"key":"BF02591885_CR5","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF01584991","volume":"3","author":"B.C. Eaves","year":"1972","unstructured":"B.C. Eaves and R. Saigal, \u201cHomotopies for computation of fixed points on unbounded regions\u201d,Mathematical Programming 3 (1972) 225\u2013237.","journal-title":"Mathematical Programming"},{"key":"BF02591885_CR6","unstructured":"D.M. Himmelblau, \u201cA uniform evaluation of constrained optimization techniques\u201d, in: F. Lootsma, ed.,Numerical methods for nonlinear optimization (Academic Press, 1972)."},{"key":"BF02591885_CR7","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1137\/0713041","volume":"13","author":"R.B. Kellogg","year":"1976","unstructured":"R.B. Kellogg, T.Y. Li and Y. Yorke, \u201cA constructive proof of the Brouwer fixed point theorem and computational results\u201d,SIAM Journal of Numerical Analysis 13 (1976) 473\u2013483.","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"BF02591885_CR8","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01585103","volume":"24","author":"M. Kojima","year":"1982","unstructured":"M. Kojima and Y. Yamamoto, \u201cVariable dimension algorithms: Basic theory, interpretations and extensions of some existing methods\u201d,Mathematical Programming 24 (1982) 177\u2013215.","journal-title":"Mathematical Programming"},{"key":"BF02591885_CR9","series-title":"Discussion Paper 151 (82-18)","volume-title":"A unified approach to several restart fixed point algorithms for their implementation and a new variable dimension algorithm","author":"M. Kojima","year":"1982","unstructured":"M. Kojima and Y. Yamamoto, \u201cA unified approach to several restart fixed point algorithms for their implementation and a new variable dimension algorithm\u201d, Discussion Paper 151 (82-18), Institute for Socio-Economic Planning, University of Tsukuba (Sakura, Japan, April 1982, revised May 1983)."},{"key":"BF02591885_CR10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/BFb0064322","volume-title":"Functional differential equations and approximations of fixed points","author":"G. Laan van der","year":"1979","unstructured":"G. van der Laan and A.J.J. Talman, \u201cA restart algorithm without an artificial level for computing fixed points on unbounded regions\u201d, in: H.-O. Peitgen and H.-O. Walther, eds.,Functional differential equations and approximations of fixed points (Springer, Berlin, 1979) pp. 247\u2013256."},{"key":"BF02591885_CR11","first-page":"3","volume-title":"Numerical solution of highly nonlinear problems","author":"G. Laan van der","year":"1980","unstructured":"G. van der Laan and A.J.J. Talman, \u201cConvergence and properties of recent variable dimension algorithms\u201d, in: W. Forster, ed.,Numerical solution of highly nonlinear problems (North-Holland, Amsterdam, 1980), pp. 3\u201336."},{"key":"BF02591885_CR12","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1007\/BF01588323","volume":"18","author":"G. Laan van der","year":"1980","unstructured":"G. van der Laan and A.J.J. Talman, \u201cAn improvement of fixed point algorithms by using a good triangulation\u201d,Mathematical Programming 18 (1980) 274\u2013285.","journal-title":"Mathematical Programming"},{"key":"BF02591885_CR13","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF01589331","volume":"20","author":"G. Laan van der","year":"1981","unstructured":"G. van der Laan and A.J.J. Talman, \u201cA class of simplicial restart fixed point algorithms without an extra dimension\u201d,Mathematical Programming 20 (1981) 33\u201348.","journal-title":"Mathematical Programming"},{"key":"BF02591885_CR14","volume-title":"Applications and extensions of an algorithm that computes fixed points of certain upper semi-continuous point to set mapping","author":"O.H. Merrill","year":"1972","unstructured":"O.H. Merrill, \u201cApplications and extensions of an algorithm that computes fixed points of certain upper semi-continuous point to set mapping\u201d, Ph.D. Thesis, University of Michigan (Ann Arbor, Michigan, 1972)."},{"key":"BF02591885_CR15","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1287\/moor.6.1.129","volume":"6","author":"P.M. Reiser","year":"1981","unstructured":"P.M. Reiser, \u201cA modified integer labelling for complementarity algorithms\u201d,Mathematics of Operations Research 6 (1981) 129\u2013139.","journal-title":"Mathematics of Operations Research"},{"key":"BF02591885_CR16","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1287\/moor.2.2.108","volume":"2","author":"R. Saigal","year":"1977","unstructured":"R. Saigal, \u201cOn the convergence rate of algorithms for solving equations that are based on complementarity pivoting\u201d,Mathematics of Operations Research 2 (1977) 108\u2013124.","journal-title":"Mathematics of Operations Research"},{"key":"BF02591885_CR17","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1287\/moor.8.4.557","volume":"8","author":"R. Saigal","year":"1983","unstructured":"R. Saigal, \u201cA homotopy for solving large, sparse and structured fixed point problems\u201d,Mathematics of Operations Research 8 (1983) 557\u2013578.","journal-title":"Mathematics of Operations Research"},{"key":"BF02591885_CR18","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/BF02612356","volume":"28","author":"R. Saigal","year":"1984","unstructured":"R. Saigal, \u201cComputational complexity of a piecewise linear homotopy algorithm\u201d,Mathematical Programming 28 (1984) 164\u2013173.","journal-title":"Mathematical Programming"},{"key":"BF02591885_CR19","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1137\/0715065","volume":"15","author":"R. Saigal","year":"1978","unstructured":"R. Saigal and M.J. Todd, \u201cEfficient acceleration techniques for fixed point algorithms\u201d,SIAM Journal of Numerical Analysis 15 (1978) 997\u20131007.","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"BF02591885_CR20","series-title":"Mathematical Centre Tract","volume-title":"Variable dimension fixed point algorithms and triangulations","author":"A.J.J. Talman","year":"1980","unstructured":"A.J.J. Talman, \u201cVariable dimension fixed point algorithms and triangulations\u201d, Mathematical Centre Tract 128 (Mathematisch Centrum, Amsterdam, 1980)."},{"key":"BF02591885_CR21","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BFb0120788","volume":"7","author":"M.J. Todd","year":"1978","unstructured":"M.J. Todd, \u201cImproving the convergence of fixed point algorithms\u201d,Mathematical Programming Study 7 (1978) 151\u2013169.","journal-title":"Mathematical Programming Study"},{"key":"BF02591885_CR22","first-page":"43","volume-title":"Numerical solution of highly nonlinear problems","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd, \u201cGlobal and local convergence and monotonicity results for a recent variable-dimension simplicial algorithm\u201d, in: W. Forster, ed.,Numerical solution of highly nonlinear problems (North-Holland, Amsterdam, 1980), pp. 43\u201369."},{"key":"BF02591885_CR23","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BFb0063203","volume-title":"Topics in Numerical Analysis","author":"M.J. Todd","year":"1982","unstructured":"M.J. Todd, \u201cAn introduction to piecewise-linear homotopy algorithms for solving systems of equations\u201d, in: A. Dold and B. Eckman, eds.,Topics in Numerical Analysis (Springer, Berlin, 1982), pp. 149\u2013202."},{"key":"BF02591885_CR24","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1287\/moor.6.4.579","volume":"6","author":"M.J. Todd","year":"1981","unstructured":"M.J. Todd, Approximate labelling for simplicial algorithms and two classes of special subsets of the sphere\u201d,Mathematics of Operations Research 6 (1981) 579\u2013592.","journal-title":"Mathematics of Operations Research"},{"key":"BF02591885_CR25","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/BF01584229","volume":"21","author":"A.H. Wright","year":"1981","unstructured":"A.H. Wright, \u201cThe octahedral algorithm, a new simplicial fixed point algorithm\u201d,Mathematical Programming 21 (1981) 47\u201369.","journal-title":"Mathematical Programming"},{"key":"BF02591885_CR26","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF02594783","volume":"25","author":"Y. Yamamoto","year":"1983","unstructured":"Y. Yamamoto, \u201cA new variable dimension algorithm for the fixed point problems\u201d,Mathematical Programming 25 (1983) 329\u2013342.","journal-title":"Mathematical Programming"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02591885.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02591885\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02591885","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T23:37:50Z","timestamp":1558395470000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02591885"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,10]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1984,10]]}},"alternative-id":["BF02591885"],"URL":"https:\/\/doi.org\/10.1007\/bf02591885","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,10]]}}}