J. F. Benders, "Partitioning procedures for solving mixed-variables programming problems," Numer. Math., vol. 4, pp. 238--252, 1962. Home/Search Document Not in Database Summary Related Articles Check |
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Dynamic scheduling: State of the art report - Kocjan (2002) (1 citation) (Correct)
....to row generation in contrast to column generation. The unimodular probing method described in Section 4.3 is such a row generation method. Another form of hybridization based master slave problem concept is Benders decomposition. The idea of Benders decomposition was rst presented in [Ben62] and generalized in [Geo72] Integration of Benders decomposition and constraint programming was described in [EW01] and [Tho01] The classical Benders decomposition is presented below. Consider the linear program P given by; P : min f c i y i subject to G i x A i y i b i 8i (4.6) ....
J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4:238-252, 1962.
Global Optimization For Constrained Nonlinear Programming - Wang (2001) (5 citations) (Correct)
....MINLP in a Lagrangian formulation and then decomposes it into subproblems in such a way that, after fixing a subset of the variables, the resulting subproblem is convex and can be solved easily. There are three methods to implement this approach. 47 Generalized Benders decomposition (GBD) [67, 77, 29] computes at each iteration an upper bound on the solution sought by solving a primal problem and a lower bound on a master problem. The primal problem corresponds to the original problem with fixed discrete variables, while the master problem is derived through nonlinear duality theory. The ....
J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numer. Math, pages 238--242, 1962.
Optimal Anytime Search For Constrained Nonlinear Programming - Chen (2001) (4 citations) (Correct)
....easily. Although these methods may not require the derivatives of continuous subproblems, di#erentiability can help improve solution time and quality. For this reason, we classify these methods under this class. There are three types of these methods. a) Generalized Benders decomposition (GBD) [64, 71, 44] computes at each iteration an upper bound on the solution sought by solving a primal problem and a lower bound on a master problem. The primal problem corresponds to the original problem with fixed discrete variables, whereas master problem is derived through nonlinear duality theory. Its major ....
J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numer. Math, pages 238--242, 1962.
Integrated Planning and Operations for Supply Chain Management - Andrew Schaefer Jayant (Correct)
....have a significantly more (or less) adverse impact on future decisions. We thus need to look at the intrinsic value of each remnant piece and to do this we define a corresponding dual problem. In order to solve the problem we therefore choose a different approach, namely, Benders decomposition [5]. The basic idea is to decompose the problem into hard variables (the integer z variables) and easy variables (the continuous variables) and alternate between solving a linear program and an integer program at each iteration. To apply Benders method, we first consider the above IP but for a ....
Benders, J.F., 1962, Partitioning Procedures for Solving Mixed-Variables Programming Problems," Numerische Mathematik , 4, 238-252.
The Theory And Applications Of Discrete Constrained Optimization.. - Wu (2000) (1 citation) (Correct)
....constrained MINLP in a Lagrangian formulation before decomposing it into subproblems in such a way that after 51 fixing a subset of the variables, the resulting subproblem is convex and can be solved easily. There are three classes of these algorithms. a) Generalized Benders Decomposition (GBD) [56, 71, 21] is used to solve a subclass of constrained MINLPs under some convexity assumptions. For example, it requires the continuous subspace to be a nonempty and convex set and the objective and constraint functions to be convex. Its basic idea is to generate in each iteration an upper bound on the ....
J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numer. Math, pages 238--242, 1962.
Optimal Investment in Capacity Expansion of Arcs in Stochastic.. - Wollmer (Correct)
....The first stage consists of one inequality which specifies that the total investment cannot exceed the fixed budget. The second stage is an arc chain formulation for maximizing total flow of all commodities. A technique developed by Van Slyke and Wets [1] which in turn is based on Bender s [2] decomposition method, is used. However, it is specialized to exploit the special structure of this problem. The solution technique involves first choosing an arbitrary solution to the first stage constraint. Then the second stage program is solved to obtain an expected value for the objective ....
Benders, J. F., "Partitioning Procedures for Solving Mixed-Variables Programming Problems, Num. Math, 4, pp. 238-252, 1962.
Improving Constrained Nonlinear Search Algorithms Through.. - Zhang (2001) (Correct)
....is convex in a subspace and can be solved easily. Although these methods may not require the di#erentiability of functions, derivative information can help improve solution time and quality significantly. There are three types of these methods. 29 Generalized Benders decomposition (GBD) [60, 68, 37] generates in each iteration an upper bound on the solution sought by solving a primal problem and a lower bound on a master problem. The primal problem corresponds to the original problem with fixed discrete variables and provides upper bound information and Lagrange multipliers for each ....
J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numer. Math, pages 238--242, 1962.
Alternating Directions Methods for the Parallel.. - Spyridon.. (Correct)
....of the basis inverse. Indirect methods essentially follow the forkjoin protocol, by decomposing the original problem into decoupled first level subproblems and then solving a master coordination problem. Eckstein [27] surveys parallel implementations to date. The Dantzig Wolfe [19] and Benders [7] decomposition are two classic indirect methods. When applied to (CBA) both can be implemented in parallel, since each block can be assigned to a PE. In the fork phase each PE solves the associated subproblem; then, in the join, a PE collects subproblem solution information, partially redefines ....
J.F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4:238--252, 1962.
Hybrid Benders Decomposition Algorithms in Constraint Logic.. - Eremin, Wallace (2001) (1 citation) Self-citation (Benders) (Correct)
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J. F. Benders. Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik, 4:238-252, 1962.
Logic-Based Benders Decomposition - Hooker, Ottosson (1995) (2 citations) Self-citation (Benders) (Correct)
....few components. This research was partially supported by U.S. Oce of Naval Research Grant N0001495 1 0517 and by the Engineering Design Research Center at Carnegie Mellon University, an Engineering Research Center of the National Science Foundation, under grant EEC8943164. Benders decomposition [7, 17] uses a problem solving strategy that can be generalized to a larger context. It assigns some of the variables trial values and nds the best solution consistent with these values. In the process it learns something about the quality of other trial solutions. It uses this information to reduce the ....
Benders, J. F., Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik 4 (1962) 238-252.
Benders Decomposition for Stochastic Programming with GAMS - Kalvelagen (2003) Self-citation (Benders) (Correct)
....equivalent problem: x p(#)d # y # Ax = b T# x W# y # = h# 0, y # (3) Date: 17 januari 2003. The structure of equation T# x W# y # = h# is called L shaped, which can be made visible by writing it out: 4) TK x WK y K = hK 2. Benders Algorithm The Benders algorithm[1, 6] to solve this problem can be formulated as follows (we largely follow the notation in[5] Step 1: Initialization # : 1 Iteration number UB : # Upper LB : # Lower Solve initial master problem: Ax = b (5) Step 2: Sub problems for # ## do Solve the sub problem: min d ....
J. F. Benders, Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik 4 (1962), 238--252.
A Global BMI Algorithm Based on the Generalized Benders.. - Beran, Vandenberghe.. (1997) (8 citations) Self-citation (Benders) (Correct)
....small rectangular bounds. For some specific classes of BMI problems, for example the low order controller design problem, heuristic specialized methods with local convergence have been developed [BG96] The method presented in this paper uses a technique called generalized Benders decomposition [Ben62, Geo72]. It can be interpreted as an extension of the GOP algorithm of Visweswaran and Floudas[FV93, VFIP96] which is a global optimization method for bilinear and biconvex optimization problems. The outline of the paper is as follows. In the next section we present the duality theory, which provides ....
J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4:238--252, 1962.
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J. F. Benders, "Partitioning procedures for solving mixed-variables programming problems," Numer. Math., vol. 4, pp. 238--252, 1962.
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J.F. Benders. Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik, 4, 1962.
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Benders, J.F., "Partitioning procedures for solving mixed variables programming problems", Numerische Mathematik 4, (1962), pp 238-252.
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J.F. Benders. Partitioning procedures for solving mixedvariable programming problems. Numerische Matematik, 4:238252, 1962.
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J.F. Benders. Partitioning procedures for solving mixed-variable programming problems. Numer. Math., 4:238-252, 1962.
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J. F. Benders. Partitioning procedures for solving mixed-variable programming problems. Numer. Math., 4:238-252, 1962.
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J.F. Benders. Partitioning procedures for solving mixed{variable programming problems. Numerische Matematik, 4:238-252, 1962.
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J. F. Benders. Partitioning procedures for solving mixed-variable programming problems. Numer. Math., 4:238-252, 1962.
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Benders, J.F. (1962): Partitioning Procedures for Solving Mixed-Variable Programming Problems, Numerische Mathematic 4, 238-252.
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J. F. Benders, 1962. Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik 4, 238-252.
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J. F. Benders. Partitioning procedures for solving mixed variable programming problems. Numerische Mathematik, 4:238--252, 1962.
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J. Benders, Partitioning procedures for solving mixed-variables mathematical programming problems. Numersche Mathematik, 4 (3): 238-252, 1960.
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Benders, J.F. (1962). Partitioning Procedures for Solving Mixed-Variables Programming Problems. Numerische Mathematic 4, 238-252.
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