메뉴 건너뛰기




Volumn 74, Issue 1, 1996, Pages 47-54

Complexity of some cutting plane methods that use analytic centers

Author keywords

Analytic center; Cutting plane methods; Nondifferentiable optimization; Potential function

Indexed keywords


EID: 0041064217     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02592145     Document Type: Article
Times cited : (4)

References (17)
  • 1
    • 0030106916 scopus 로고    scopus 로고
    • A note on some analytic center cutting plane methods for convex feasibility and minimization problems
    • A. Altman and K.C. Kiwiel, A note on some analytic center cutting plane methods for convex feasibility and minimization problems, Computational Optimization and Applications 5 (1996) 175-180.
    • (1996) Computational Optimization and Applications , vol.5 , pp. 175-180
    • Altman, A.1    Kiwiel, K.C.2
  • 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 69 (1995) 1-43.
    • (1995) Mathematical Programming , vol.69 , pp. 1-43
    • Atkinson, D.S.1    Vaidya, P.M.2
  • 4
    • 0029336061 scopus 로고
    • A cutting plane method from analytic centers for stochastic programming
    • O. Bahn, O. du Merle, J.-L. Goffin and J.-Ph. Vial, A cutting plane method from analytic centers for stochastic programming, Mathematical Programming 69 (1995) 45-73.
    • (1995) Mathematical Programming , vol.69 , pp. 45-73
    • Bahn, O.1    Du Merle, O.2    Goffin, J.-L.3    Vial, J.-Ph.4
  • 5
    • 43949150075 scopus 로고
    • Implementation and behavior of an interior point cutting plane algorithm for convex programming: An application to geometric programming
    • [51 O. Bahn, J.-L. Goffin, J.-Ph. Vial and O. du Merle, Implementation and behavior of an interior point cutting plane algorithm for convex programming: An application to geometric programming, Discrete Applied Mathematics 49 (1993) 3-23.
    • (1993) Discrete Applied Mathematics , vol.49 , pp. 3-23
    • Bahn, O.1    Goffin, J.-L.2    Vial, J.-Ph.3    Du Merle, O.4
  • 7
    • 0000949338 scopus 로고
    • Decomposition and nondifferentiable optimization with the projective algorithm
    • J.-L. Goffin, A. Haurie and J.-Ph. Vial, Decomposition and nondifferentiable optimization with the projective algorithm, Management Science 37 (1992) 284-302.
    • (1992) Management Science , vol.37 , pp. 284-302
    • Goffin, J.-L.1    Haurie, A.2    Vial, J.-Ph.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, Dordrecht
    • J.-L. Goffin, Z.-Q. Luo and Y. Ye, On the complexity of a column generation algorithm for convex or quasiconvex feasibility problems, in: W.W. Hager, D.W. Hearn and P.M. Pardalos, eds., Large Scale Optimization: State of the Art (Kluwer Academic Publishers, Dordrecht, 1994), 182-191.
    • (1994) Large Scale Optimization: State of the Art , pp. 182-191
    • Goffin, J.-L.1    Luo, Z.-Q.2    Ye, Y.3
  • 9
    • 0030303856 scopus 로고    scopus 로고
    • Complexity analysis of an interior point cutting plane method for convex feasibility problems
    • to appear
    • J.-L. Goffin, Z.-Q. Luo and Y. Ye, Complexity analysis of an interior point cutting plane method for convex feasibility problems, SIAM Journal on Optimization (1996), to appear.
    • (1996) SIAM Journal on Optimization
    • Goffin, J.-L.1    Luo, Z.-Q.2    Ye, Y.3
  • 10
    • 0031531864 scopus 로고    scopus 로고
    • Efficiency of the analytic center cutting plane method for convex minimization
    • to appear
    • K.C. Kiwiel, Efficiency of the analytic center cutting plane method for convex minimization, SIAM Journal on Optimization (1996), to appear.
    • (1996) SIAM Journal on Optimization
    • Kiwiel, K.C.1
  • 12
    • 0012036999 scopus 로고
    • A long-step, cutting plane algorithm for linear and convex programming
    • Dept. of Decision Sciences & Engg. Systems, Rensselaer Polytechnic Institute, Troy, NY, Aug. revised Aug.
    • J.E. Mitchell and S. Ramaswamy, A long-step, cutting plane algorithm for linear and convex programming, DSES Technical Report No. 37-93-387, Dept. of Decision Sciences & Engg. Systems, Rensselaer Polytechnic Institute, Troy, NY, Aug. 1993; revised Aug. 1994.
    • (1993) DSES Technical Report No. 37-93-387
    • Mitchell, J.E.1    Ramaswamy, S.2
  • 13
    • 0029338609 scopus 로고
    • Complexity estimates of some cutting plane methods based on the analytic barrier
    • Yu.E. Nesterov, Complexity estimates of some cutting plane methods based on the analytic barrier, Mathematical Programming 69 (1995) 149-176.
    • (1995) Mathematical Programming , vol.69 , pp. 149-176
    • Nesterov, Yu.E.1
  • 15
    • 0001668563 scopus 로고
    • New algorithms in convex programming based on the notion of 'centre' (for systems of analytic inequalities) and on rational extrapolation
    • K.H. Hoffman, J.-B. Hiriart-Urruty, C. Lemaréchal and J. Zowe, eds., Birkhäuser, Basel
    • G. Sonnevend, New algorithms in convex programming based on the notion of 'centre' (for systems of analytic inequalities) and on rational extrapolation, in: K.H. Hoffman, J.-B. Hiriart-Urruty, C. Lemaréchal and J. Zowe, eds., Trends in Mathematical Optimization, International Series of Numerical Mathematics 84 (Birkhäuser, Basel, 1988), 311-326.
    • (1988) Trends in Mathematical Optimization, International Series of Numerical Mathematics , vol.84 , pp. 311-326
    • Sonnevend, G.1
  • 16
    • 0003036055 scopus 로고
    • A potential reduction algorithm allowing column generation
    • Y. Ye, A potential reduction algorithm allowing column generation, SIAM Journal on Optimization 2 (1992) 7-20.
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 7-20
    • Ye, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.