On Decomposition Methods for a Class of Partially Separable Nonlinear Programs

Published Online:https://doi.org/10.1287/moor.1070.0282

References

  • Alexandrov N. M., Hussaini M. Y.Multidisciplinary Design Optimization: State of the Art (1997) (SIAM, Philadelphia) Google Scholar
  • Alexandrov N. M., Lewis R. M. Analytical and computational aspects of collaborative optimization. (2000) . Technical Report TM-2000-210104, NASA, Hampton, VAGoogle Scholar
  • Benders J. F. Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik (1962) 4:238–252CrossrefGoogle Scholar
  • Birge J. R., Louveaux F.Introduction to Stochastic Programming (1997) (Springer-Verlag, New York) Google Scholar
  • Braun R. D. Collaborative optimization: An architecture for large-scale distributed design. (1996) . Doctoral dissertation, Stanford University, Standford, CAGoogle Scholar
  • Braun R. D., Kroo I. M., Alexandrov N. M., Hussaini M. Y. Development and application of the collaborative optimization architecture in a multidisciplinary design environment. Multidisciplinary Design Optimization: State of the Art (1997) (SIAM, Philadelphia) 98–116Google Scholar
  • Byrd R. H., Hribar M. E., Nocedal J. An interior point algorithm for large-scale nonlinear programming. SIAM J. Optim. (1999) 9:877–900CrossrefGoogle Scholar
  • Chun B. J., Robinson S. M. Scenario analysis via bundle decomposition. Ann. Oper. Res. (1995) 56:39–63CrossrefGoogle Scholar
  • Cohen G., Miara B. Optimization with an auxiliary constraint and decomposition. SIAM J. Control Optim. (1990) 28(1):137–157CrossrefGoogle Scholar
  • Colson B., Marcotte P., Savard G. Bilevel programming: A survey. 4OR (2005) 3:87–107CrossrefGoogle Scholar
  • Cottle R. W. Manifestations of the Schur complement. Linear Algebra Appl. (1974) 8:189–211CrossrefGoogle Scholar
  • Cramer E. J., Dennis J. E., Frank P. D., Lewis R. M., Shubin G. R. Problem formulation for multidisciplinary optimization. SIAM J. Optim. (1994) 4(4):754–776CrossrefGoogle Scholar
  • DeMiguel V., Murray W. An analysis of collaborative optimization methods. Eighth AIAA/USAF/NASA/ISSMO Sympos. Multidisciplinary Anal. and Optim. (2000) Long Beach, CA(AIAA, Reston, VA) . Paper 00-4720CrossrefGoogle Scholar
  • DeMiguel V., Murray W. A local convergence analysis of bilevel decomposition algorithms. Optim. Engrg. (2006) 7:99–133CrossrefGoogle Scholar
  • Dempe S.Foundations of Bilevel Programming (2002) (Kluwer Academic Publishers, Boston) Google Scholar
  • El-Bakry A. S., Tapia R. A., Tsuchiya T., Zhang Y. On the formulation and theory of Newton interior-point method for nonlinear programming. J. Optim. Theory Appl. (1996) 89:507–541CrossrefGoogle Scholar
  • Fiacco A. V., McCormick G. P.Nonlinear Programming: Sequential Unconstrained Minimization Techniques (1968) (John Wiley and Sons, New York) Google Scholar
  • Forsgren A., Gill P. E. Primal-dual interior methods for nonconvex nonlinear programming. SIAM J. Optim. (1998) 8(4):1132–1152CrossrefGoogle Scholar
  • Gay D. M., Overton M. L., Wright M. H. A primal-dual interior method for nonconvex nonlinear programming. (1997) . Technical Report 97-4-08, Computing Sciences Research, Bell Laboratories, Murray Hill, NJGoogle Scholar
  • Geoffrion A. M. Generalized Benders decomposition. J. Optim. Theory Appl. (1972) 10(4):237–260CrossrefGoogle Scholar
  • Gould N. I. M., Orban D., Sartenaer A., Toint P. L. Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. SIAM J. Optim. (2001) 11(4):974–1002CrossrefGoogle Scholar
  • Haftka R. T., Sobieszczanski-Sobieski J. Multidisciplinary aerospace design optimization: Survey of recent developments. Structural Optim. (1997) 14:1–23CrossrefGoogle Scholar
  • Helgason T., Wallace S. W. Approximate scenario solutions in the progressive hedging algorithm. Ann. Oper. Res. (1991) 31:425–444CrossrefGoogle Scholar
  • Martinez H. H., Parada Z., Tapia R. A. On the characterization of q-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming. Boletín de la Sociedad Matemática Mexicana (1995) 1:1–12Google Scholar
  • Medhi D. Parallel bundle-based decomposition for large-scale structured mathematical programming problems. Ann. Oper. Res. (1990) 22:101–127CrossrefGoogle Scholar
  • Raghunathan A. U., Biegler L. T. Interior point methods for mathematical programs with complementarity constraints. (2003) . Technical report, Department of Chemical Engineering, Carnegie Mellon University, PittsburghGoogle Scholar
  • Robinson S. M., Prekopa A., Szelezsan J., Strazicky B. Bundle-based decomposition: Description and preliminary results. System Modelling and Optimization. Lecture Notes in Control and Information Sciences (1986) (Springer-Verlag, Berlin) 751–756CrossrefGoogle Scholar
  • Rockafellar R. T., Wets R. J.-B. Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. (1991) 16:119–147LinkGoogle Scholar
  • Ruszczynski A. A regularized decomposition for minimizing a sum of polyhedral functions. Math. Programming (1986) 35:309–333CrossrefGoogle Scholar
  • Ruszczynski A. On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math. Oper. Res. (1995) 20(3):634–656LinkGoogle Scholar
  • Shimizu K., Ishizuka Y., Bard J. F.Nondifferentiable and Two-Level Mathematical Programming (1997) (Kluwer Academic Publishers, Boston) CrossrefGoogle Scholar
  • Tammer K., Guddat J., Jongen H., Kummer B., Nozicka F. The application of parametric optimization and imbedding for the foundation and realization of a generalized primal decomposition approach. Parametric Optimization and Related Topics, Mathematical Research (1987) 35(Akademie-Verlag, Berlin) 376–386Google Scholar
  • Van Slyke R., Wets R. J.-B. L-shaped linear programs with application to optimal control and stochastic programming. SIAM J. Appl. Math. (1969) 17:638–663CrossrefGoogle Scholar
  • Vanderbei R. J., Shanno D. F. An interior-point algorithm for nonconvex nonlinear programming. (1997) . Technical Report SOR-97-21, Statistics and Operations Research, Princeton University, Princeton, NJGoogle Scholar
  • Vicente L. N., Wright S. J. Local convergence of a primal-dual method for degenerate nonlinear programming. Computational Optim. Appl. (2002) 22:311–328CrossrefGoogle Scholar
  • Yamashita H., Yabe H. Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization. Math. Programming (1996) 75:377–397CrossrefGoogle Scholar
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