An Analytic Center Cutting Plane Approach for Conic Programming

Published Online:https://doi.org/10.1287/moor.1080.0319

References

  • Atkinson D. S., Vaidya P. M. A cutting plane algorithm for convex programming that uses analytic centers. Math. Programming (1995) 69:1–43CrossrefGoogle Scholar
  • Belloni A., Freund R. M., Vempala S. An efficient re-scaled perceptron algorithm for conic systems. (2006) . Technical report, IBM T.J. Watson Research Center, Yorktown Heights, NYGoogle Scholar
  • Chua S. K., Toh K. C., Zhao G. Y. An analytic center cutting plane method with deep cuts for semidefinite feasibility problems. J. Optim. Theory Appl. (2004) 123:291–318CrossrefGoogle Scholar
  • Faybusovich L., Tsuchiya T. Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank. Math. Programming (2003) 97(3):471–493CrossrefGoogle Scholar
  • Goffin J.-L., Vial J.-P. Multiple cuts in the analytic center cutting plane method. SIAM J. Optim. (2001) 11(1):266–288CrossrefGoogle Scholar
  • Goffin J.-L., Vial J.-P. Convex nondifferentiable optimization: A survey focussed on the analytic center cutting plane method. Optim. Methods Software (2002) 17(5):805–867CrossrefGoogle Scholar
  • Güler O. Barrier functions in interior point methods. Math. Oper. Res. (1996) 21(4):860–885LinkGoogle Scholar
  • Hauser R., Güler O. Self-scaled barrier on symmetric cones and their classification. Foundations Computational Math. (2002) 2(2):121–143CrossrefGoogle Scholar
  • Helmberg C., Rendl F. A spectral bundle method for semidefinite programming. SIAM J. Optim. (2000) 10(3):673–696CrossrefGoogle Scholar
  • Krishnan K., Mitchell J. E. A unifying framework for several cutting plane methods for semidefinite programming. Optim. Methods Software (2006) 21(1):57–74CrossrefGoogle Scholar
  • Luo Z.-Q., Sun J. An analytic center based column generation algorithm for convex quadratic feasibility problems. SIAM J. Optim. (1999) 9:217–235CrossrefGoogle Scholar
  • Lüthi H.-J., Büeller B. The analytic center quadratic cut method (ACQCM) for strongly monotone variational inequality problems. SIAM J. Optim. (2000) 10(2):415–426CrossrefGoogle Scholar
  • Mitchell J. E. Polynomial interior point cutting plane methods. Optim. Methods Software (2003) 18(5):507–534CrossrefGoogle Scholar
  • Mitchell J. E., Ramaswamy S. A long-step, cutting plane algorithm for linear and convex programming. Ann. Oper. Res. (2000) 99:95–122CrossrefGoogle Scholar
  • Mitchell J. E., Todd M. J. Solving combinatorial optimization problems using Karmarkar's algorithm. Math. Programming (1992) 56(3):245–284CrossrefGoogle Scholar
  • Mokhtarian F. S., Goffin J.-L. An analytic center quadratic cut method for the convex quadratic feasibility problem. Math. Programming (2002) 93(2):305–325CrossrefGoogle Scholar
  • Nesterov Y. E. Smoothing technique and its applications in semidefinite programming. Math. Programming (2007) 110(2):245–259CrossrefGoogle Scholar
  • Nesterov Y. E., Nemirovskii A. S.Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms (1993) (SIAM Publications, SIAM, Philadelphia) Google Scholar
  • Nesterov Y. E., Todd M. J. Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. (1997) 22:1–42LinkGoogle Scholar
  • Oskoorouchi M. R., Goffin J.-L. The analytic center cutting plane method with semidefinite cuts. SIAM J. Optim. (2003) 13(4):1029–1053CrossrefGoogle Scholar
  • Oskoorouchi M. R., Goffin J.-L. An interior point cutting plane method for the convex feasibility problem with second-order cone inequalities. Math. Oper. Res. (2005) 30(1):127–149LinkGoogle Scholar
  • Oskoorouchi M. R., Mitchell J. E. A second-order cone cutting surface method: Complexity and application. (2005) . Techncial report, College of Business Administration, California State University, San Marcos, CA, http://www.rpi.edu/ mitchj/papers/socr.htmlGoogle Scholar
  • Renegar J.A Mathematical View of Interior-Point Methods in Convex Optimization (2001) 1(SIAM, Philadelphia) MPS-SIAM Series on OptimizationCrossrefGoogle Scholar
  • Renegar J. Hyperbolic programs, and their derivative relaxations. Foundations Computational Math. (2006) 6(1):59–79CrossrefGoogle Scholar
  • Schmieta S., Alizadeh F. Associative and Jordan algebras, and polynomial time interior point algorithms for symmetric cones. Math. Oper. Res. (2001) 26(3):543–564LinkGoogle Scholar
  • Schmieta S., Alizadeh F. Extension of primal-dual interior point algorithms to symmetric cones. Math. Programming (2003) 96(3):409–438CrossrefGoogle Scholar
  • Sivaramakrishnan K. K., Plaza G., Terlaky T. A conic interior point decomposition approach for large scale semidefinite programming. (2005) . Technical report, Department of Mathematics, North Carolina State University, Raleigh, NC, http://www4.ncsu.edu/∼kksivara/publications/conic-ipm-decomposition.pdfGoogle Scholar
  • Sonnevend G. New algorithms in convex programming based on a notion of center and on rational extrapolations. Internat. Ser. Numer. Math. (1988) 84:311–327Google Scholar
  • Sun J., Toh K. C., Zhao G. Y. An analytic center cutting plane method for semidefinite feasibility problems. Math. Oper. Res. (2002) 27:332–346LinkGoogle Scholar
  • Toh K. C., Zhao G., Sun J. A multiple-cut analytic center cutting plane method for semidefinite feasibility problems. SIAM J. Optim. (2002) 12(4):1126–1146CrossrefGoogle Scholar
  • Tunçel L., Nemirovski A. Self-concordant barriers for convex approximations of structured convex sets. (2007) . Technical report CORR 2007–03, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, CanadaGoogle Scholar
  • Ye Y. Complexity analysis of the analytic center cutting plane method that uses multiple cuts. Math. Programming (1997) 78:85–104CrossrefGoogle Scholar
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