메뉴 건너뛰기




Volumn 15, Issue 2, 2000, Pages 167-191

Polynomial cutting surfaces algorithm for the convex feasibility problem defined by self-concordant inequalities

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; ITERATIVE METHODS; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

EID: 0033875233     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008787027641     Document Type: Article
Times cited : (15)

References (20)
  • 3
    • 0029340922 scopus 로고
    • A cutting plane algorithm for convex programming that uses analytic centers
    • D.S. Atkinson and P.M. Vaidya, "A cutting plane algorithm for convex programming that uses analytic centers," Mathematical Programming, vol. 69, pp. 1-44, 1995.
    • (1995) Mathematical Programming , vol.69 , pp. 1-44
    • Atkinson, D.S.1    Vaidya, P.M.2
  • 4
    • 43949150075 scopus 로고
    • Experimental behavior of an interior point cutting plane algorithm for convex programming: An application to geometric programming
    • O. Bahn, O. Du Merle, J.-L. Goffin, and J.-P. Vial, "Experimental behavior of an interior point cutting plane algorithm for convex programming: an application to geometric programming," Discrete Applied Mathematics, vol. 49, pp. 3-23, 1994.
    • (1994) Discrete Applied Mathematics , vol.49 , pp. 3-23
    • Bahn, O.1    Du Merle, O.2    Goffin, J.-L.3    Vial, J.-P.4
  • 5
    • 0029336061 scopus 로고
    • A cutting plane method from analytic centers for stochastic programming
    • O. Bahn, O. Du Merle, J.-L. Goffin, and J.-P. Vial, "A cutting plane method from analytic centers for stochastic programming," Mathematical Programming, vol. 69, pp. 45-74, 1995.
    • (1995) Mathematical Programming , vol.69 , pp. 45-74
    • Bahn, O.1    Du Merle, O.2    Goffin, J.-L.3    Vial, J.-P.4
  • 6
    • 0029338698 scopus 로고
    • A sufficient condition for self-concordance, with application to some classes of structured convex programming problems
    • D. den Hertog, F. Jarre, C. Roos, and T. Terlaky, "A sufficient condition for self-concordance, with application to some classes of structured convex programming problems," Mathematical Programming, vol. 69, pp. 75-88, 1995.
    • (1995) Mathematical Programming , vol.69 , pp. 75-88
    • Den Hertog, D.1    Jarre, F.2    Roos, C.3    Terlaky, T.4
  • 7
    • 0030303856 scopus 로고    scopus 로고
    • Complexity analysis of an interior cutting plane method for convex feasibility problems
    • J.-L. Goffin, Z.-Q. Luo, and Y. Ye, "Complexity analysis of an interior cutting plane method for convex feasibility problems," SIAM J. Optimization, vol. 6, pp. 638-652, 1996.
    • (1996) SIAM J. Optimization , vol.6 , pp. 638-652
    • Goffin, J.-L.1    Luo, Z.-Q.2    Ye, Y.3
  • 8
    • 0039877123 scopus 로고
    • On the complexity of a column generation algorithm for convex or quasiconvex feasibility problems
    • W.W. Hager, D.W. Hearn, and P.M. Pardalos, (Eds.), Kluwer Academic Publishers B.V.
    • J.-L. Goffin, Z.-Q. Luo, and Y Ye, "On the complexity of a column generation algorithm for convex or quasiconvex feasibility problems," in Large Scale Optimization: State of the Art, W.W. Hager, D.W. Hearn, and P.M. Pardalos, (Eds.), Kluwer Academic Publishers B.V., 1994, pp. 182-189.
    • (1994) Large Scale Optimization: State of the Art , pp. 182-189
    • Goffin, J.-L.1    Luo, Z.-Q.2    Ye, Y.3
  • 10
    • 0003849384 scopus 로고
    • Ph.D. Thesis, Institut für Angwandte Mathematik und Statistik, Universität Würtzburg, Germany
    • F. Jarre, The Method of Analytic Centers for Smooth Convex Programs, Ph.D. Thesis, Institut für Angwandte Mathematik und Statistik, Universität Würtzburg, Germany, 1989.
    • (1989) The Method of Analytic Centers for Smooth Convex Programs
    • Jarre, F.1
  • 11
    • 0031285914 scopus 로고    scopus 로고
    • Analysis of a cutting plane method that uses weighted analytic center and multiple cuts
    • Z.-Q. Luo, "Analysis of a cutting plane method that uses weighted analytic center and multiple cuts," SIAM Journal on Optimization, vol. 7, pp. 697-716, 1997.
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 697-716
    • Luo, Z.-Q.1
  • 12
    • 0041125582 scopus 로고    scopus 로고
    • An analytic center based column generation algorithm for the convex quadratic feasibility problem
    • Z.-Q. Luo and J. Sun, "An analytic center based column generation algorithm for the convex quadratic feasibility problem," SIAM J. Optimization, vol. 9, no. 1, pp. 217-235, 1998.
    • (1998) SIAM J. Optimization , vol.9 , Issue.1 , pp. 217-235
    • Luo, Z.-Q.1    Sun, J.2
  • 13
    • 0004683784 scopus 로고
    • An interior point algorithm for solving smooth convex programs based on Newton's method
    • S. Mehrotra and J. Sun, "An interior point algorithm for solving smooth convex programs based on Newton's method," Contemporary Mathematics, vol. 114, pp. 265-284, 1990.
    • (1990) Contemporary Mathematics , vol.114 , pp. 265-284
    • Mehrotra, S.1    Sun, J.2
  • 14
    • 0026123776 scopus 로고
    • On computing the center of a convex quadratically constrained set
    • S. Mehrotra and J. Sun, "On computing the center of a convex quadratically constrained set," Mathematical Programming, vol. 50, pp. 81-89, 1991.
    • (1991) Mathematical Programming , vol.50 , pp. 81-89
    • Mehrotra, S.1    Sun, J.2
  • 15
    • 0029338609 scopus 로고
    • Cutting plane algorithms from analytic centers: Efficiency estimates
    • Y. Nesterov, "Cutting plane algorithms from analytic centers: efficiency estimates," Mathematical Programming, vol. 69, pp. 149-176, 1995.
    • (1995) Mathematical Programming , vol.69 , pp. 149-176
    • Nesterov, Y.1
  • 17
    • 0003150632 scopus 로고
    • A quadratically convergent method for minimizing a sum of euclidean norms
    • M.L. Overton, "A quadratically convergent method for minimizing a sum of euclidean norms," Mathematical Programming, vol. 27, pp. 34-63, 1983.
    • (1983) Mathematical Programming , vol.27 , pp. 34-63
    • Overton, M.L.1
  • 18
    • 0001668563 scopus 로고
    • New algorithms in convex programming based on a notion of 'centre' (for systems of analytic inequalities) and on rational extrapolation
    • K.H. Hoffmann, J.B. Hiriat-Urruty, C. Lemarechal, and J. Zowe, (Eds.), Germany
    • G. Sonnevend, "New algorithms in convex programming based on a notion of 'centre' (for systems of analytic inequalities) and on rational extrapolation," in Trends in Mathematical Optimization: Proceedings of the 4th French-German Conference on Optimization in Irsee, K.H. Hoffmann, J.B. Hiriat-Urruty, C. Lemarechal, and J. Zowe, (Eds.), Germany, 1986.
    • (1986) Trends in Mathematical Optimization: Proceedings of the 4th French-German Conference on Optimization in Irsee
    • Sonnevend, G.1
  • 19
    • 0003036055 scopus 로고
    • A potential reduction algorithm allowing column generation
    • Y. Ye, "A potential reduction algorithm allowing column generation," SIAM Journal on Optimization, vol. 2, pp. 7-20, 1992.
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 7-20
    • Ye, Y.1
  • 20
    • 0002392220 scopus 로고    scopus 로고
    • Complexity analysis of the analytic center cutting plane method that uses multiple cuts
    • Y. Ye, "Complexity analysis of the analytic center cutting plane method that uses multiple cuts," Mathematical Programming, vol. 78, pp. 85-104, 1997.
    • (1997) Mathematical Programming , vol.78 , pp. 85-104
    • Ye, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.