{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:27:51Z","timestamp":1759847271061},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","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\/bf02612336","type":"journal-article","created":{"date-parts":[[2007,4,27]],"date-time":"2007-04-27T06:50:56Z","timestamp":1177656656000},"page":"288-328","source":"Crossref","is-referenced-by-count":25,"title":["A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm"],"prefix":"10.1007","volume":"28","author":[{"given":"Masakazu","family":"Kojima","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshitsugu","family":"Yamamoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02612336_CR1","first-page":"36","volume-title":"Continuation methods","author":"J.C. Alexander","year":"1978","unstructured":"J.C. Alexander, \u201cThe topological theory of an embedding method\u201d, in: H. Wacker, ed.,Continuation methods (Academic Press, New York, 1978) pp. 36\u201367."},{"key":"BF02612336_CR2","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1137\/1022003","volume":"22","author":"E. Allgower","year":"1980","unstructured":"E. Allgower and K. Georg, \u201cSimplicial and continuation methods for approximating fixed points and solutions to systems of equations\u201d,SIAM Review 22 (1980) 28\u201385.","journal-title":"SIAM Review"},{"key":"BF02612336_CR3","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF02234051","volume":"8","author":"E. Allgower","year":"1971","unstructured":"E. Allgower and C.L. Keller, \u201cA search routine for a Sperner simplex\u201d,Computing 8 (1971) 157\u2013165.","journal-title":"Computing"},{"key":"BF02612336_CR4","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1093\/imamat\/11.3.317","volume":"11","author":"L.C.W. Dixon","year":"1973","unstructured":"L.C.W. Dixon, \u201cConjugate directions without linear searches\u201d,Journal of the Institute of Mathematics and Its Applications 11 (1973) 317\u2013328.","journal-title":"Journal of the Institute of Mathematics and Its Applications"},{"key":"BF02612336_CR5","doi-asserted-by":"crossref","DOI":"10.21236\/ADA089990","volume-title":"Variable-dimension complexes with applications","author":"R.M. Freund","year":"1980","unstructured":"R.M. Freund, \u201cVariable-dimension complexes with applications\u201d, Ph.D. Dissertation, Stanford University, (Stanford, CA, 1980)."},{"key":"BF02612336_CR6","volume-title":"On tracing an implicitly defined curve by quasi-Newton steps and calculating bifurcation by local perturbations","author":"K. Georg","year":"1980","unstructured":"K. Georg, \u201cOn tracing an implicitly defined curve by quasi-Newton steps and calculating bifurcation by local perturbations\u201d, University of Bonn (Bonn, 1980)."},{"key":"BF02612336_CR7","first-page":"37","volume-title":"Numerical solution of highly nonlinear problems, fixed point algorithms and complementarity problems","author":"M. Kojima","year":"1980","unstructured":"M. Kojima, \u201cA note on \u2018A new algorithm for computing fixed points\u2019 by van der Laan and Talman\u201d, in: W. Forster, ed.,Numerical solution of highly nonlinear problems, fixed point algorithms and complementarity problems (North-Holland, New York, 1980) pp. 37\u201342."},{"key":"BF02612336_CR8","series-title":"Lecture Notes in Mathematics","first-page":"199","volume-title":"Numerical solution of nonlinear equations","author":"M. Kojima","year":"1980","unstructured":"M. Kojima, \u201cAn introduction to variable dimension algorithms for solving systems of equations\u201d, in: E.L. Allgower, K. Glashoff and H.-O. Peitgen, eds.Numerical solution of nonlinear equations, Lecture Notes in Mathematics 878 (Springer, Berlin, 1980) pp. 199\u2013237."},{"key":"BF02612336_CR9","series-title":"Research Reports on Information Sciences","volume-title":"Variable dimension algorithms, Part II: Some new algorithms and triangulations with continuous refinement of mesh size","author":"M. Kojima","year":"1980","unstructured":"M. Kojima and Y. Yamamoto, \u201cVariable dimension algorithms, Part II: Some new algorithms and triangulations with continuous refinement of mesh size\u201d, Research Reports on Information Sciences B-82, Department of Information Sciences, Tokyo Institute of Technology (Tokyo, 1980)."},{"key":"BF02612336_CR10","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":"BF02612336_CR11","first-page":"2","volume-title":"Computing methods in optimization problems","author":"H.W. Kuhn","year":"1969","unstructured":"H.W. Kuhn, \u201cApproximate search for fixed points\u201d, in:Computing methods in optimization problems 2 (Academic Press, New York, 1969)."},{"key":"BF02612336_CR12","volume-title":"Simplicial fixed point algorithms","author":"G. Laan van der","year":"1980","unstructured":"G. van der Laan, \u201cSimplicial fixed point algorithms\u201d, Ph.D. Dissertation, Free University (Amsterdam, 1980)."},{"key":"BF02612336_CR13","volume-title":"On the computation of fixed points in the product space of the unit simplices and an application to noncooperativen-person games","author":"G. Laan van der","year":"1978","unstructured":"G. van der Laan and A.J.J. Talman, \u201cOn the computation of fixed points in the product space of the unit simplices and an application to noncooperativen-person games\u201d, Free University (Amsterdam, 1978)."},{"key":"BF02612336_CR14","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1007\/BF01588226","volume":"17","author":"G. Laan van der","year":"1979","unstructured":"G. van der Laan and A.J.J. Talman, \u201cA restart algorithm for computing fixed point without extra dimension\u201d,Mathematical Programming 17 (1979) 74\u201384.","journal-title":"Mathematical Programming"},{"key":"BF02612336_CR15","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/BFb0064322","volume-title":"Functional differential equations and approximation 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 approximation of fixed points, Lecture Notes in Mathematics 730 (Springer, Berlin, 1979) pp. 247\u2013256."},{"key":"BF02612336_CR16","first-page":"3","volume-title":"Numerical solution of highly nonlinear problems, fixed point algorithms and complementarity 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, fixed point algorithms and complementarity problems (North-Holland, New York, 1980) pp. 3\u201336."},{"key":"BF02612336_CR17","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":"BF02612336_CR18","volume-title":"Simplicial algorithms for finding stationary points, a unifying description","author":"G. Laan van der","year":"1982","unstructured":"G. van der Laan and A.J.J. Talman, \u201cSimplicial algorithms for finding stationary points, a unifying description\u201d, Free University (Amsterdam, 1982)."},{"key":"BF02612336_CR19","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/B978-0-12-590240-3.50008-2","volume-title":"Analysis and computation of fixed points","author":"T.Y. Li","year":"1980","unstructured":"T.Y. Li and J.A. Yorke, \u201cA simple reliable numerical algorithm for following homotopy paths\u201d, in: S.M. Robinson, ed.,Analysis and computation of fixed points (Academic Press, New York, 1980) pp. 73\u201391."},{"key":"BF02612336_CR20","volume-title":"Applications and extensions of an algorithm that computes fixed points of a certain upper semicontinuous 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 a certain upper semicontinuous point to set mapping\u201d, Ph.D. Dissertation, University of Michigan (MI, 1972)."},{"key":"BF02612336_CR21","first-page":"129","volume":"6","author":"R.M. Reiser","year":"1981","unstructured":"R.M. Reiser, \u201cA modified integer labelling for complementarity algorithms\u201d,Mathematical Programming 6 (1981) 129\u2013139.","journal-title":"Mathematical Programming"},{"key":"BF02612336_CR22","volume-title":"A homotopy for solving large, sparse and structured fixed point problems","author":"R. Saigal","year":"1981","unstructured":"R. Saigal, \u201cA homotopy for solving large, sparse and structured fixed point problems\u201d, Northwestern University (Evanston, IL, 1981)."},{"key":"BF02612336_CR23","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/B978-0-12-358350-5.50012-9","volume-title":"Mathematical Programming","author":"L.S. Shapley","year":"1973","unstructured":"L.S. Shapley, \u201cOn balanced games without side payments\u201d, in: T.C. Hu and S.M. Robinson, eds.,Mathematical Programming (Academic Press, New York, 1973) pp. 261\u2013290."},{"key":"BF02612336_CR24","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, Ph.D. Dissertation, Free University (Amsterdam, 1980)."},{"key":"BF02612336_CR25","series-title":"Lecture Notes in Economics and Mathematical Systems","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-50327-6","volume-title":"The computation of fixed points and applications","author":"M.J. Todd","year":"1976","unstructured":"M.J. Todd,The computation of fixed points and applications, Lecture Notes in Economics and Mathematical Systems (Springer, New York, 1976)."},{"key":"BF02612336_CR26","series-title":"Technical Report","volume-title":"Fixed-point algorithms that allow restarting without an extra dimension","author":"M.J. Todd","year":"1978","unstructured":"M.J. Todd, \u201cFixed-point algorithms that allow restarting without an extra dimension\u201d, Technical Report No. 379, School of Operations Research and Industrial Engineering, Cornell University (Ithaca, NY, 1978)."},{"key":"BF02612336_CR27","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1287\/moor.5.2.242","volume":"5","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd, \u201cTraversing large pieces of linearity in algorithms that solve equations by following piecewise-linear paths\u201d,Mathematics of Operations Research 5 (1980) 242\u2013257.","journal-title":"Mathematics of Operations Research"},{"key":"BF02612336_CR28","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/BF01588321","volume":"18","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd, \u201cExploiting structure in piecewise-linear homotopy algorithms for solving equations\u201d,Mathematical Programming 18 (1980) 233\u2013247.","journal-title":"Mathematical Programming"},{"key":"BF02612336_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/B978-0-12-590240-3.50005-7","volume-title":"Analysis and computation of fixed points","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd, \u201cNumerical stability and sparsity in piecewise-linear algorithms\u201d, in: S.M. Robinson, ed.,Analysis and computation of fixed points (Academic Press, New York, 1980) pp. 1\u201324."},{"key":"BF02612336_CR30","first-page":"43","volume-title":"Numerical solution of highly nonlinear problems, fixed point algorithms and complementarity 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, fixed point algorithms and complementarity problems (North-Holland, New York, 1980) pp. 43\u201369."},{"key":"BF02612336_CR31","series-title":"Technical Report","volume-title":"Piecewise-linear homotopy algorithms for sparse systems of nonlinear equations","author":"M.J. Todd","year":"1981","unstructured":"M.J. Todd, \u201cPiecewise-linear homotopy algorithms for sparse systems of nonlinear equations\u201d, Technical Report No. 527, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, 1981)."},{"key":"BF02612336_CR32","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1080\/01630568008816052","volume":"2","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd and A.H. Wright, \u201cA variable-dimension simplicial algorithm for antipodal fixed-point theorems\u201d,Numerical Functional Analysis and Optimization 2 (1980) 155\u2013186.","journal-title":"Numerical Functional Analysis and Optimization"},{"key":"BF02612336_CR33","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":"BF02612336_CR34","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 problem\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\/BF02612336.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02612336\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02612336","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T08:34:25Z","timestamp":1558341265000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02612336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,10]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1984,10]]}},"alternative-id":["BF02612336"],"URL":"https:\/\/doi.org\/10.1007\/bf02612336","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,10]]}}}