Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets

References

  • Balas E., Ceria S., Cornuéjols G. A lift-and-project cutting plane algorithm for mixed 0-1 programs. Math. Programming (1993) 58:295–323CrossrefGoogle Scholar
  • Kojima M., Tunçel L. Cones of matrices and successive convex relaxations of nonconvex sets. SIAM J. Optim. (2000a) 10:750–778CrossrefGoogle Scholar
  • Kojima M. Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems. Math. Programming (2000b) 89:79–111CrossrefGoogle Scholar
  • Kojima M., Matsumoto T., Shida M. Moderate nonconvexity = convexity + quadratic concavity. (1999) . Technical report B-348, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo, JapanGoogle Scholar
  • Lovász L., Schrijver A. Cones of matrices and set functions and 0-1 optimization. SIAM J. Optim. (1991) 1:166–190CrossrefGoogle Scholar
  • Horst R., Tuy H.Global Optimization, Second, Revised Edition (1992) (Springer-Verlag, Berlin. Germany) Google Scholar
  • Sherali H. D., Adams W. P. A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Disc. Math. (1990) 3:411–430CrossrefGoogle Scholar
  • Sherali H. D., Adams H. D., Adams W. P. A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems. Disc. Appl. Math. (1994) 52:83–106CrossrefGoogle Scholar
  • Sherali H. D., Almeddine. A new reformulation-linearization technique for bilinear programming problems. J. Global Optim. (1992) 2:379–410CrossrefGoogle Scholar
  • Sherali H. D., Tuncbilek C. H. A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique. J. Global Optim. (1992) 2:101–112CrossrefGoogle Scholar
  • Sherali H. D. A reformulation-convexification approach for solving nonconvex quadratic programming problems. J. Global Optim. (1995) 7:1–31CrossrefGoogle Scholar
  • Shor N. Z. Dual quadratic estimates in polynomial and boolean programming. Ann. Oper. Res. (1990) 25:163–168CrossrefGoogle Scholar
  • Takeda A., Dai Y., Fukuda M., Kojima M., Pardalos P. M. Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems. Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems (2000) (Kluwer Academic Publishers)489–510CrossrefGoogle Scholar
  • Tunçel L., Xu S. Complexity analyses of discretized successive convex relaxation methods. . CORR 99-37, Dept. of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, CanadaGoogle Scholar
  • Tuy H.Convex analysis and Global Optimization (1998) (Kluwer, Dordrecht, The Netherlands) CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.