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Volumn 124, Issue 1-2, 2000, Pages 245-261

Piecewise linear methods for nonlinear equations and optimization

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER GRAPHICS; NONLINEAR EQUATIONS; OPTIMIZATION;

EID: 0034538701     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00427-1     Document Type: Article
Times cited : (22)

References (37)
  • 1
    • 12444345572 scopus 로고
    • Estimates for piecewise linear approximations of implicitly defined manifolds
    • E.L. Allgower K. Georg Estimates for piecewise linear approximations of implicitly defined manifolds Appl. Math. Lett. 1 5 1989 1 7
    • (1989) Appl. Math. Lett. , vol.1 , Issue.5 , pp. 1-7
    • Allgower, E.L.1    Georg, K.2
  • 2
    • 85119555799 scopus 로고    scopus 로고
    • E.L. Allgower, K. Georg, Numerical Continuation Methods: An Introduction, Series in Computational Mathematics, Vol. 13, Springer, Berlin, 1990, p. 388.
  • 3
    • 70350662980 scopus 로고    scopus 로고
    • Numerical path following
    • E.L. Allgower K. Georg Numerical path following P.G. Ciarlet J.L. Lions Handbook of Numerical Analysis, Vol. 5 1997 North-Holland Amsterdam 3 207
    • (1997) , pp. 3-207
    • Allgower, E.L.1    Georg, K.2
  • 5
    • 0023329383 scopus 로고
    • An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces
    • E.L. Allgower S. Gnutzmann An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces SIAM J. Numer. Anal. 24 1987 452 469
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 452-469
    • Allgower, E.L.1    Gnutzmann, S.2
  • 6
    • 0022048415 scopus 로고
    • An algorithm for piecewise-linear approximation of an implicitly defined manifold
    • E.L. Allgower Ph.H. Schmidt An algorithm for piecewise-linear approximation of an implicitly defined manifold SIAM J. Numer. Anal. 22 1985 322 346
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 322-346
    • Allgower, E.L.1    Schmidt, Ph.H.2
  • 7
    • 85119561531 scopus 로고    scopus 로고
    • J. Bloomenthal Introduction to Implicit Surfaces 1997 Morgan Kaufmann San Francisco
    • (1997)
    • Bloomenthal, J.1
  • 8
    • 0000014724 scopus 로고
    • Optimality and degeneracy in linear programming
    • A. Charnes Optimality and degeneracy in linear programming Econometrica 20 1952 160 170
    • (1952) Econometrica , vol.20 , pp. 160-170
    • Charnes, A.1
  • 9
    • 0012072679 scopus 로고
    • Solution rays for a class of complementarity problems
    • R.W. Cottle Solution rays for a class of complementarity problems Math. Programming Study 1 1974 58 70
    • (1974) Math. Programming Study , vol.1 , pp. 58-70
    • Cottle, R.W.1
  • 11
    • 0000243546 scopus 로고
    • Discrete groups generated by reflections
    • H.S.M. Coxeter Discrete groups generated by reflections Ann. Math. 6 1934 13 29
    • (1934) Ann. Math. , vol.6 , pp. 13-29
    • Coxeter, H.S.M.1
  • 12
    • 85119565363 scopus 로고
    • H.S.M. Coxeter Regular Polytopes 3rd ed 1963 MacMillan New York
    • (1963)
    • Coxeter, H.S.M.1
  • 13
    • 0025417986 scopus 로고
    • On the computation of manifolds of fold points for parameter-dependent problems
    • R.-X. Dai W.C. Rheinboldt On the computation of manifolds of fold points for parameter-dependent problems SIAM J. Numer. Anal. 27 1990 437 466
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 437-466
    • Dai, R.-X.1    Rheinboldt, W.C.2
  • 14
    • 85119564131 scopus 로고
    • C. Dang Triangulations and Simplicial Methods Lecture Notes in Economics and Mathematical Systems 1995 Springer Berlin
    • (1995)
    • Dang, C.1
  • 15
    • 0032073820 scopus 로고    scopus 로고
    • A simplicial approach to integer programming
    • C. Dang H. van Maaren A simplicial approach to integer programming Math. Oper. Res. 23 1998 403 415
    • (1998) Math. Oper. Res. , vol.23 , pp. 403-415
    • Dang, C.1    van Maaren, H.2
  • 16
    • 85119556073 scopus 로고
    • G.B. Dantzig Linear Programming and Extensions 1963 Princeton University Press Princeton, NJ
    • (1963)
    • Dantzig, G.B.1
  • 17
    • 34250452611 scopus 로고
    • Homotopies for the computation of fixed points
    • B.C. Eaves Homotopies for the computation of fixed points Math. Programming 3 1972 1 22
    • (1972) Math. Programming , vol.3 , pp. 1-22
    • Eaves, B.C.1
  • 18
    • 0012226424 scopus 로고
    • A short course in solving equations with PL homotopies
    • B.C. Eaves A short course in solving equations with PL homotopies R.W. Cottle C.E. Lemke Nonlinear Programming, SIAM-AMS Proceedings, Vol. 9 1976 American Mathematical Society Providence, RI 73 143
    • (1976) , pp. 73-143
    • Eaves, B.C.1
  • 19
    • 85119553475 scopus 로고
    • B.C. Eaves A Course in Triangulations for Solving Equations with Deformations Lecture Notes in Economics and Mathematical Systems Vol. 234 1984 Springer Berlin
    • (1984)
    • Eaves, B.C.1
  • 20
    • 34250456846 scopus 로고
    • Homotopies for computation of fixed points on unbounded regions
    • B.C. Eaves R. Saigal Homotopies for computation of fixed points on unbounded regions Math. Programming 3 1972 225 237
    • (1972) Math. Programming , vol.3 , pp. 225-237
    • Eaves, B.C.1    Saigal, R.2
  • 21
    • 0001696328 scopus 로고
    • Simplizialzerlegungen von beschränkter Flachheit
    • H. Freudenthal Simplizialzerlegungen von beschränkter Flachheit Ann. Math. 43 1942 580 582
    • (1942) Ann. Math. , vol.43 , pp. 580-582
    • Freudenthal, H.1
  • 22
    • 0040725599 scopus 로고
    • Approximation of integrals for boundary element methods
    • K. Georg Approximation of integrals for boundary element methods SIAM J. Sci. Statist. Comput. 12 1991 443 453
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 443-453
    • Georg, K.1
  • 23
    • 0032382631 scopus 로고    scopus 로고
    • Intersection theorems with a continuum of intersection points
    • P.J.J. Herings A.J.J. Talman Intersection theorems with a continuum of intersection points J. Optim. Theory Appl. 96 1998 311 335
    • (1998) J. Optim. Theory Appl. , vol.96 , pp. 311-335
    • Herings, P.J.J.1    Talman, A.J.J.2
  • 24
    • 85119562223 scopus 로고    scopus 로고
    • A. Kirman (Ed.) Elements of General Equilibrium Analysis 1998 Blackwell Oxford
    • (1998)
    • Kirman (Ed.), A.1
  • 25
    • 85119552280 scopus 로고
    • M. Kojima N. Megiddo T. Noma A. Yoshise A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems Lecture Notes in Computer Science Vol. 538 1991 Springer Berlin
    • (1991)
    • Kojima, M.1    Megiddo, N.2    Noma, T.3    Yoshise, A.4
  • 26
    • 0001644591 scopus 로고
    • Bimatrix equilibrium points and mathematical programming
    • C.E. Lemke Bimatrix equilibrium points and mathematical programming Management Sci. 11 1965 681 689
    • (1965) Management Sci. , vol.11 , pp. 681-689
    • Lemke, C.E.1
  • 27
    • 0000176346 scopus 로고
    • Equilibrium points of bimatrix games
    • C.E. Lemke J.T. Howson Equilibrium points of bimatrix games SIAM J. Appl. Math. 12 1964 413 423
    • (1964) SIAM J. Appl. Math. , vol.12 , pp. 413-423
    • Lemke, C.E.1    Howson, J.T.2
  • 28
    • 85119552598 scopus 로고    scopus 로고
    • O. Merrill, Applications and extensions of an algorithm that computes fixed points of a certain upper semi-continuous point to set mapping, Ph.D. Thesis, University of Michigan, Ann Arbor, MI, 1972.
  • 29
    • 85119565330 scopus 로고
    • Yu.E. Nesterov A. Nemirovskii Interior-Point Polynomial Algorithms in Convex Programming 1993 SIAM Philadelphia, PA
    • (1993)
    • Nesterov, Yu.E.1    Nemirovskii, A.2
  • 30
    • 0000256568 scopus 로고
    • On the computation of multi-dimensional solution manifolds of parameterized equations
    • W.C. Rheinboldt On the computation of multi-dimensional solution manifolds of parameterized equations Numer. Math. 53 1988 165 182
    • (1988) Numer. Math. , vol.53 , pp. 165-182
    • Rheinboldt, W.C.1
  • 31
    • 33646992093 scopus 로고
    • Efficient acceleration techniques for fixed point algorithms
    • R. Saigal M.J. Todd Efficient acceleration techniques for fixed point algorithms SIAM J. Number. Anal. 15 1978 997 1007
    • (1978) SIAM J. Number. Anal. , vol.15 , pp. 997-1007
    • Saigal, R.1    Todd, M.J.2
  • 32
    • 0001310049 scopus 로고
    • The approximation of fixed points of a continuous mapping
    • H.E. Scarf The approximation of fixed points of a continuous mapping SIAM J. Appl. Math. 15 1967 1328 1343
    • (1967) SIAM J. Appl. Math. , vol.15 , pp. 1328-1343
    • Scarf, H.E.1
  • 33
    • 85119550737 scopus 로고
    • H.E. Scarf T. Hansen The Computation on Economic Equilibria 1973 Yale University Press New Haven, CT
    • (1973)
    • Scarf, H.E.1    Hansen, T.2
  • 34
    • 85119558031 scopus 로고
    • M.J. Todd The Computation of Fixed Points and Applications Lecture Notes in Economics and Mathematical Systems Vol. 124 1976 Springer Berlin
    • (1976)
    • Todd, M.J.1
  • 35
    • 0020721793 scopus 로고
    • Piecewise-linear homotopy algorithms for sparse systems of nonlinear equations
    • M.J. Todd Piecewise-linear homotopy algorithms for sparse systems of nonlinear equations SIAM J. Control Optim. 21 1983 204 214
    • (1983) SIAM J. Control Optim. , vol.21 , pp. 204-214
    • Todd, M.J.1
  • 36
    • 85119556703 scopus 로고    scopus 로고
    • G. van der Laan, A.J.J. Talman, Z. Yang, Existence and approximation of robust stationary points on polytopes, SIAM J. Control Optim., in preparation.
  • 37
    • 85119558929 scopus 로고    scopus 로고
    • S.J. Wright Primal–Dual Interior-Point Methods 1997 SIAM Philadelphia, PA
    • (1997)
    • Wright, S.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.