Journal ArticleDOI
On the convergence of cross decomposition
TLDR
Finite convergence of the algorithm equipped with some simple convergence tests has been proved and using the stronger convergence tests finite exact convergence is shown in the first cases.Abstract:
Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence. In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.read more
Citations
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Journal ArticleDOI
The Benders decomposition algorithm: A literature review
Ragheb Rahmaniani,Ragheb Rahmaniani,Teodor Gabriel Crainic,Teodor Gabriel Crainic,Michel Gendreau,Michel Gendreau,Walter Rei,Walter Rei +7 more
TL;DR: A state-of-the-art survey of the Benders Decomposition algorithm, emphasizing its use in combinatorial optimization and introducing a taxonomy of algorithmic enhancements and acceleration strategies based on the main components of the algorithm.
Journal ArticleDOI
Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decomposition
TL;DR: In this article, the optimal lot-sizing of the replenishments has a cumulative effect on practical economic production quantity (EPQ) models with the aim of inventory system management.
Journal ArticleDOI
Accelerating Benders Decomposition by Local Branching
TL;DR: This paper shows how local branching can be used to accelerate the classical Benders decomposition algorithm by applying local branching throughout the solution process, and shows how Benders feasibility cuts can be strengthened or replaced with local branching constraints.
Journal ArticleDOI
Global optimization of MINLP problems in Process Synthesis and Design
TL;DR: Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear αBB,SMIN-αBB, and the General structure MixedInteger Nonlinear βBB,GMIN-βBB, are presented.
DissertationDOI
Relaxation and decomposition methods for mixed integer nonlinear programming
TL;DR: The LaGO library is an Object-Oriented Library for Solving MINLPs and provides an overview of global Optimization methods, algorithms, and concepts.
References
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Book
Linear Programming and Extensions
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Journal ArticleDOI
Partitioning procedures for solving mixed-variables programming problems
TL;DR: In this article, the 8th International Meeting of the Institute of Management Sciences, Brussels, August 23-26, 1961, the authors presented a paper entitled "The International Journal of Management Science and Management Sciences".
Journal ArticleDOI
Linear Programming and Extensions. George B. Dantzig. Pp. xvi, 623. 92/- (Princeton Univ. Press). 1963
Journal ArticleDOI
Decomposition Principle for Linear Programs
George B. Dantzig,Philip Wolfe +1 more
TL;DR: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.
Journal ArticleDOI
Generalized Benders decomposition
TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.