On Decomposition Methods for a Class of Partially Separable Nonlinear Programs
Published Online:1 Feb 2008https://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
- Analytical and computational aspects of collaborative optimization. (2000) . Technical Report TM-2000-210104, NASA, Hampton, VAGoogle Scholar
- Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik (1962) 4:238–252Crossref, Google Scholar
- Introduction to Stochastic Programming (1997) (Springer-Verlag, New York) Google Scholar
- Collaborative optimization: An architecture for large-scale distributed design. (1996) . Doctoral dissertation, Stanford University, Standford, CAGoogle Scholar
- , 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
- An interior point algorithm for large-scale nonlinear programming. SIAM J. Optim. (1999) 9:877–900Crossref, Google Scholar
- Scenario analysis via bundle decomposition. Ann. Oper. Res. (1995) 56:39–63Crossref, Google Scholar
- Optimization with an auxiliary constraint and decomposition. SIAM J. Control Optim. (1990) 28(1):137–157Crossref, Google Scholar
- Bilevel programming: A survey. 4OR (2005) 3:87–107Crossref, Google Scholar
- Manifestations of the Schur complement. Linear Algebra Appl. (1974) 8:189–211Crossref, Google Scholar
- Problem formulation for multidisciplinary optimization. SIAM J. Optim. (1994) 4(4):754–776Crossref, Google Scholar
- An analysis of collaborative optimization methods. Eighth AIAA/USAF/NASA/ISSMO Sympos. Multidisciplinary Anal. and Optim. (2000) Long Beach, CA(AIAA, Reston, VA) . Paper 00-4720Crossref, Google Scholar
- A local convergence analysis of bilevel decomposition algorithms. Optim. Engrg. (2006) 7:99–133Crossref, Google Scholar
- Foundations of Bilevel Programming (2002) (Kluwer Academic Publishers, Boston) Google Scholar
- On the formulation and theory of Newton interior-point method for nonlinear programming. J. Optim. Theory Appl. (1996) 89:507–541Crossref, Google Scholar
- Nonlinear Programming: Sequential Unconstrained Minimization Techniques (1968) (John Wiley and Sons, New York) Google Scholar
- Primal-dual interior methods for nonconvex nonlinear programming. SIAM J. Optim. (1998) 8(4):1132–1152Crossref, Google Scholar
- A primal-dual interior method for nonconvex nonlinear programming. (1997) . Technical Report 97-4-08, Computing Sciences Research, Bell Laboratories, Murray Hill, NJGoogle Scholar
- Generalized Benders decomposition. J. Optim. Theory Appl. (1972) 10(4):237–260Crossref, Google Scholar
- Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. SIAM J. Optim. (2001) 11(4):974–1002Crossref, Google Scholar
- Multidisciplinary aerospace design optimization: Survey of recent developments. Structural Optim. (1997) 14:1–23Crossref, Google Scholar
- Approximate scenario solutions in the progressive hedging algorithm. Ann. Oper. Res. (1991) 31:425–444Crossref, Google Scholar
- 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
- Parallel bundle-based decomposition for large-scale structured mathematical programming problems. Ann. Oper. Res. (1990) 22:101–127Crossref, Google Scholar
- Interior point methods for mathematical programs with complementarity constraints. (2003) . Technical report, Department of Chemical Engineering, Carnegie Mellon University, PittsburghGoogle Scholar
- , 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) 751–756Crossref, Google Scholar
- Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. (1991) 16:119–147Link, Google Scholar
- A regularized decomposition for minimizing a sum of polyhedral functions. Math. Programming (1986) 35:309–333Crossref, Google Scholar
- On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math. Oper. Res. (1995) 20(3):634–656Link, Google Scholar
- Nondifferentiable and Two-Level Mathematical Programming (1997) (Kluwer Academic Publishers, Boston) Crossref, Google Scholar
- , 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
- L-shaped linear programs with application to optimal control and stochastic programming. SIAM J. Appl. Math. (1969) 17:638–663Crossref, Google Scholar
- An interior-point algorithm for nonconvex nonlinear programming. (1997) . Technical Report SOR-97-21, Statistics and Operations Research, Princeton University, Princeton, NJGoogle Scholar
- Local convergence of a primal-dual method for degenerate nonlinear programming. Computational Optim. Appl. (2002) 22:311–328Crossref, Google Scholar
- Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization. Math. Programming (1996) 75:377–397Crossref, Google Scholar

