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  A log-barrier method with Benders decomposition for solving two-stage stochastic programs (1997) [8 citations — 5 self]

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by Gongyun Zhao
Mathematical Programming 90
http://www.math.nus.edu.sg/~matzgy/papers/lbbdsp.ps
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Abstract:

An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time.

Citations

195 Interior-point polynomial algorithms in convex programming – Nesterov, Nemirovskii - 1994
175 On the implementation of a (primal-dual) interior point method – Mehrotra - 1992
113 Stochastic Programming – Kall, Wallace - 1994
77 Scenarios and policy aggregation in optimization under uncertainty – Rockafellar, Wets - 1991
70 Decomposition and partitioning methods for multistage stochastic linear programs – Birge - 1985
69 L-shaped linear programs with applications to optimal control and stochastic programming – SLYKE, WETS - 1969
58 Stochastic decomposition: an algorithm for two-stage linear programs with recourse – Higle, Sen - 1991
58 A new scenario decomposition method for large-scale stochastic optimization – Mulvey, Ruszczynski - 1995
52 Computing block-angular Karmarkar projections with applications to stochastic programming – BIRGE, QI - 1988
52 Decomposition and nondifferentiable optimization with the projective algorithm – Goffin, Haurie, et al. - 1992
45 A cutting plane method from analytic centers for stochastic programming – BAHN, MERLE, et al. - 1995
41 a computer code for the multistage stochastic linear programming problem – MSLIP - 1990
41 New algorithms in convex programming based on a notion of center and – Sonnevend - 1988
33 An “analytic” center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming – Sonnevend
27 Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs – Infanger - 1994
26 A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs – Birge, Donohue, et al. - 1996
26 Cutting plane algorithms from analytic centers: efficiency estimates – Nesterov - 1995
21 Applying the progressive hedging algorithm to stochastic generalized networks – Mulvey, Vladimirou - 1991
20 Efficient solution of two-stage stochastic linear programs with interior point methods – BIRGE, HOLMES - 1992
20 Complexity analysis of the analytic center cutting plane method that uses multiple cuts, Mathematical Programming 78 – Ye - 1997
18 A logarithmic barrier cutting plane method for convex programming – Hertog, Kaliski, et al. - 1995
16 Formulating stochastic programs for interior point methods – Lustig, Mulvey, et al. - 1991
16 A massively parallel algorithm for nonlinear stochastic network problems – Nielsen, Zenios - 1993
15 Performance of a Benchmark Parallel Implementation of the Van Slyke and Wets Algorithm for Two-stage – Ariyawansa, Hudson - 1991
15 deep and very deep cuts in the analytic center cutting plane method – Goffin, Vial - 1996
15 Interior point algorithms for linear complementarity problems based on large neighborhoods of the central path – Zhao - 1998
10 A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming – Rockafellar, Wets - 1986
9 Interior-Point Methods via Self-Concordance or Relative Lipschitz Condition – Jarre - 1994
9 Interior-point methods with decomposition for solving large-scale linear programs – Zhao - 1999
8 Current trends in stochastic programming computation and applications – Birge - 1995
8 Horizontal and vertical decomposition in interior point methods for linear programs," Working paper – Kojima, Megiddo, et al. - 1993
8 Stochastic convex programming: basic duality – Rockafellar, Wets - 1976
6 Computational methods for solving two-stage stochastic linear programming problems – Kall - 1979
6 Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticity – Stoer, Wechs - 1996
5 Proximal minimizations with D-functions and the massively parallel solution of linear stochastic network programs – Nielsen, Zenios - 1993
4 Large-scale linear programming techniques in stochastic programming – Wets - 1988
3 Warm start and ffl-subgradients in the cutting plane scheme for block-angular linear programs – Gondzio, Vial - 1997
2 A predictor-corrector method for extended linear-quadratic programming – Sun, Zhu - 1996
1 A potential-reduction algorithm for solving a linear program directly from an infeasible "warm start – Freund - 1992
1 Complexity analysis of an analytic center cutting plane method for convex feasibility problems – Goffin, Luo, et al. - 1996
1 Polynomial cuting plane algorithms for stochastic programming and related problems – Jiang - 1997