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Volumn , Issue , 2005, Pages 323-330

On algorithms for discrete and approximate Brouwer fixed points

Author keywords

Approximate fixed point; Fixed point theorem; Lipschitz function; Sperner's lemma

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING;

EID: 34848910771     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1060590.1060638     Document Type: Conference Paper
Times cited : (33)

References (42)
  • 2
    • 0001436273 scopus 로고
    • Existence of an equilibrium for a competitive economy
    • K. Arrow and G. Debreu. Existence of an equilibrium for a competitive economy. Econometrica, 22:265-290, 1954.
    • (1954) Econometrica , vol.22 , pp. 265-290
    • Arrow, K.1    Debreu, G.2
  • 3
    • 0000307498 scopus 로고
    • Sur les opérations dans les ensembles abstraits et leur application aux Équations intégrales
    • S. Banach. Sur les opérations dans les ensembles abstraits et leur application aux Équations intégrales. Fundamenta. Mathematicae, 3:133-181, 1922.
    • (1922) Fundamenta. Mathematicae , vol.3 , pp. 133-181
    • Banach, S.1
  • 4
    • 34250967150 scopus 로고
    • Über abbildung von mannigfaltigkeiten
    • L. Brouwer. Über abbildung von mannigfaltigkeiten. Mathematische Annalen, 71:97-115, 1910.
    • (1910) Mathematische Annalen , vol.71 , pp. 97-115
    • Brouwer, L.1
  • 5
    • 35048821454 scopus 로고    scopus 로고
    • Fisher equilibrium price with a class of concave utility functions
    • N. Chen, X. Deng, X. Sun, and A. C.-C. Yao. Fisher equilibrium price with a class of concave utility functions. In ESA 2004, pages 169-179.
    • ESA 2004 , pp. 169-179
    • Chen, N.1    Deng, X.2    Sun, X.3    Yao, A.C.-C.4
  • 6
    • 25144471886 scopus 로고    scopus 로고
    • Efficient computation of equilibrium prices for market with leontief utilities
    • To appear
    • B. Codenotti and K. Varadarajan. Efficient computation of equilibrium prices for market with leontief utilities. In To appear in ICALP 2004.
    • ICALP 2004
    • Codenotti, B.1    Varadarajan, K.2
  • 7
    • 0038446895 scopus 로고    scopus 로고
    • Pricing network edges for heterogeneous selfish users
    • R. Cole, Y. Dodis, and T. Roughgarden. Pricing network edges for heterogeneous selfish users. In STOC 2003, pages 521-530.
    • STOC 2003 , pp. 521-530
    • Cole, R.1    Dodis, Y.2    Roughgarden, T.3
  • 10
    • 4544235463 scopus 로고    scopus 로고
    • The spending constraint model for market equilibrium: Algorithmic, existence and uniqueness results
    • N. Devanur. The spending constraint model for market equilibrium: algorithmic, existence and uniqueness results. In STOC 2004, pages 519-528.
    • STOC 2004 , pp. 519-528
    • Devanur, N.1
  • 12
    • 34250452611 scopus 로고
    • Homotopies for computation of fixed points
    • B. Eaves. Homotopies for computation of fixed points. Mathematical Programming, 3:1-22, 1972.
    • (1972) Mathematical Programming , vol.3 , pp. 1-22
    • Eaves, B.1
  • 13
    • 38249025245 scopus 로고
    • Exponential lower bounds for finding brouwer fixed points
    • M. Hirsch, C. Papadimitriou, and S. Vavasis. Exponential lower bounds for finding brouwer fixed points. J. Complexity, 5:379-416, 1989.
    • (1989) J. Complexity , vol.5 , pp. 379-416
    • Hirsch, M.1    Papadimitriou, C.2    Vavasis, S.3
  • 14
    • 0001067246 scopus 로고    scopus 로고
    • Approximating fixed points of weakly contracting mappings
    • Z. Huang, L. Khachiyan, and K. Sikorski. Approximating fixed points of weakly contracting mappings. J. Complexity, 15:200-213, 1999.
    • (1999) J. Complexity , vol.15 , pp. 200-213
    • Huang, Z.1    Khachiyan, L.2    Sikorski, K.3
  • 15
    • 0041928145 scopus 로고    scopus 로고
    • A discrete fixed point theorem and its applications
    • T. Iimura. A discrete fixed point theorem and its applications. Journal of Mathematical Economics, 39:725-742, 2003.
    • (2003) Journal of Mathematical Economics , vol.39 , pp. 725-742
    • Iimura, T.1
  • 16
    • 30744449329 scopus 로고    scopus 로고
    • Discrete fixed point theorem reconsidered
    • T. Iimura, K. Murota, and A. Tamura. Discrete fixed point theorem reconsidered. METR, 9 2004.
    • (2004) METR , pp. 9
    • Iimura, T.1    Murota, K.2    Tamura, A.3
  • 17
    • 17744369541 scopus 로고    scopus 로고
    • A polynomial time algorithm for computing the arrow-debreu market equilibrium for linear utilities
    • K. Jain. A polynomial time algorithm for computing the arrow-debreu market equilibrium for linear utilities. In FOCS 2004, pages 286-294.
    • FOCS 2004 , pp. 286-294
    • Jain, K.1
  • 19
    • 20744437758 scopus 로고    scopus 로고
    • Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
    • K. Jain, V. Vazirani, and Y. Ye. Market equilibria for homothetic, quasi-concave utilities and economies of scale in production. In SODA 2005.
    • SODA 2005
    • Jain, K.1    Vazirani, V.2    Ye, Y.3
  • 20
    • 0016993685 scopus 로고
    • Constructive proof of the brouwer fixed point theorem and computational results
    • R. Kellogg, T. Li, and J. Yorke. Constructive proof of the brouwer fixed point theorem and computational results. SIAM J. Numer. Anal, 13:473-483, 1976.
    • (1976) SIAM J. Numer. Anal , vol.13 , pp. 473-483
    • Kellogg, R.1    Li, T.2    Yorke, J.3
  • 21
    • 0346900215 scopus 로고    scopus 로고
    • Computational complexity of fixed points and intersection points
    • K.-I. Ko. Computational complexity of fixed points and intersection points. J. Complexity, 11:265-292.
    • J. Complexity , vol.11 , pp. 265-292
    • Ko, K.-I.1
  • 22
    • 30744434731 scopus 로고
    • Über systeme von funktionen mehrerer variabeln
    • L. Kronecker. Über systeme von funktionen mehrerer variabeln. Montsh. Berl. Akad. Wiss., pages 159-163, 688-698, 1869.
    • (1869) Montsh. Berl. Akad. Wiss. , pp. 159-163
    • Kronecker, L.1
  • 24
    • 0042641574 scopus 로고    scopus 로고
    • A duality model of tcp and queue management algorithms
    • S. Low. A duality model of tcp and queue management algorithms. IEEE/ACM Transactions on Networking, 11(4):525-536, 2003.
    • (2003) IEEE/ACM Transactions on Networking , vol.11 , Issue.4 , pp. 525-536
    • Low, S.1
  • 26
    • 0039765772 scopus 로고
    • Invarianz bei linearen approximationen
    • G. Meinardus. Invarianz bei linearen approximationen. Arch. Rational. Mech. Anal., 14:301-303, 1963.
    • (1963) Arch. Rational. Mech. Anal. , vol.14 , pp. 301-303
    • Meinardus, G.1
  • 28
    • 0002021736 scopus 로고
    • Equilibrium points in n-person games
    • J. F. Nash. Equilibrium points in n-person games. In Proceedings of NAS, 1950.
    • (1950) Proceedings of NAS
    • Nash, J.F.1
  • 29
    • 0025539852 scopus 로고    scopus 로고
    • On graph-theoretic lemmata and complexity classes
    • C. Papadimitriou. On graph-theoretic lemmata and complexity classes. In STOC 1990, pages 794-801.
    • STOC 1990 , pp. 794-801
    • Papadimitriou, C.1
  • 32
    • 0001310049 scopus 로고
    • The approximation of fixed points of a continuous mapping
    • H. Scarf. The approximation of fixed points of a continuous mapping. SIAM Journal on Applied Mathematics, 15:997-1007, 1967.
    • (1967) SIAM Journal on Applied Mathematics , vol.15 , pp. 997-1007
    • Scarf, H.1
  • 33
    • 0036289698 scopus 로고    scopus 로고
    • A two-dimensional bisection envelope algorithm for fixed points
    • S. Shellman and K. Sikorski. A two-dimensional bisection envelope algorithm for fixed points. J. Complexity, 18(2):641-659, 2002.
    • (2002) J. Complexity , vol.18 , Issue.2 , pp. 641-659
    • Shellman, S.1    Sikorski, K.2
  • 34
    • 0347383275 scopus 로고    scopus 로고
    • Algorithm 825: A deep-cut bisection envelope algorithm for fixed points
    • S. Shellman and K. Sikorski. Algorithm 825: A deep-cut bisection envelope algorithm for fixed points. ACM Trans. Math. Soft., 29(3):309-325, 2003.
    • (2003) ACM Trans. Math. Soft. , vol.29 , Issue.3 , pp. 309-325
    • Shellman, S.1    Sikorski, K.2
  • 35
    • 0348233976 scopus 로고    scopus 로고
    • A recursive algorithm for the infinity-norm fixed point problem
    • S. Shellman and K. Sikorski. A recursive algorithm for the infinity-norm fixed point problem. J. Complexity, 19(6):799-834, 2003.
    • (2003) J. Complexity , vol.19 , Issue.6 , pp. 799-834
    • Shellman, S.1    Sikorski, K.2
  • 36
    • 0042783504 scopus 로고
    • Fast algorithms for the computation of fixed points
    • R. Milanese and A.Vicino, editors. Plenum Press, New York
    • K. Sikorski. Fast algorithms for the computation of fixed points. In R. Milanese and A.Vicino, editors, In Robustness in Identification and Control, pages 49-59. Plenum Press, New York, 1989.
    • (1989) Robustness in Identification and Control , pp. 49-59
    • Sikorski, K.1
  • 37
    • 0009633720 scopus 로고
    • An ellipsoid algorithm for the computation of fixed points
    • K. Sikorski, C. Tsay, and H. Wozniakowski. An ellipsoid algorithm for the computation of fixed points. J. Complexity, 9:181-200, 1993.
    • (1993) J. Complexity , vol.9 , pp. 181-200
    • Sikorski, K.1    Tsay, C.2    Wozniakowski, H.3
  • 38
    • 38249034979 scopus 로고
    • Complexity of fixed points, i
    • K. Sikorski and H. Wozniakowski. Complexity of fixed points, i. J. Complexity, 3(4):388-405, 1987.
    • (1987) J. Complexity , vol.3 , Issue.4 , pp. 388-405
    • Sikorski, K.1    Wozniakowski, H.2
  • 39
    • 49549130863 scopus 로고
    • A convergent process of price adjustment process and global newton methods
    • S. Smale. A convergent process of price adjustment process and global newton methods. Journal on Mathematical Economics, 3:107-120, 1976.
    • (1976) Journal on Mathematical Economics , vol.3 , pp. 107-120
    • Smale, S.1
  • 41
    • 0030381960 scopus 로고    scopus 로고
    • Spectral partitioning works: Planar graphs and finite element meshes
    • D. Spielman and S.-H. Teng. Spectral partitioning works: Planar graphs and finite element meshes. In FOCS 1996, pages 96-105.
    • FOCS 1996 , pp. 96-105
    • Spielman, D.1    Teng, S.-H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.