In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a ...
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We discuss a hybrid method for solving separable nonlinear integer programming problems. With the subgradient algorithm we determine a surrogate problem. This problem is solved by dynamic programming. We obtain sharp ...
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We discuss a hybrid method for solving separable nonlinear integer programming problems. With the subgradient algorithm we determine a surrogate problem. This problem is solved by dynamic programming. We obtain sharp and simple computable bounds for the branch and bound process of solving the original problem. [ABSTRACT FROM AUTHOR]
This paper describes recent experience in tackling large nonlinear integer programming problems using the MINOS large-scale optimization software. A technique is presented for extending the constrained search approach...
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Any real-valued nonlinear function in 0–1 variables can be rewritten as a multilinear function. We discuss classes of lower and upper bounding linear expressions for multilinear functions in 0–1 variables. For any m...
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Any real-valued nonlinear function in 0–1 variables can be rewritten as a multilinear function. We discuss classes of lower and upper bounding linear expressions for multilinear functions in 0–1 variables. For any multilinear inequality in 0–1 variables, we define an equivalent family of linear inequalities. This family contains the well-known system of generalized covering inequalities, as well as other linear equivalents of the multilinear inequality that are more compact, i.e., of smaller cardinality. In a companion paper [7]. we discuss dominance relations between various linear equivalents of a multilinear inequality, and describe a class of algorithms for multilinear 0–1 programming based on these results.
The purpose of this note is to present an accelerated algorithm for solving 0–1 positive polynomial (PP) problems. Like our covering relaxation algorithm (Management Science 1979), the accelerated algorithm is a cutt...
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The purpose of this note is to present an accelerated algorithm for solving 0–1 positive polynomial (PP) problems. Like our covering relaxation algorithm (Management Science 1979), the accelerated algorithm is a cutting plane method, which uses the linear set covering problem as a relaxation for PP. However, a unique and novel feature of the accelerated algorithm is that it attempts to generate cutting planes from heuristic solutions to the set covering problem whenever possible. Computational results reveal that this strategy of generating cutting planes has led to a significant reduction in the computational time required to solve a PP problem.
Systems of nonlinear equations of the form [formula omitted], where A is an m × n matrix of ratmnal constants and [formula omitted] are column vectors, are considered Each [formula omitted] is of the form [formul...
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A nonlinear integer programming model for expanding the trans- portation system of an underdeveloped country is presented. The model uses integer 0-1 decision variables. The basic model has linear con- straints and a ...
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A nonlinear integer programming model for expanding the trans- portation system of an underdeveloped country is presented. The model uses integer 0-1 decision variables. The basic model has linear con- straints and a nonlinear objective function. Seme special situations and extensions to the model are presented. The benefits being maximized in the objective function are discussed, as are the problems of param- eterization and suboptimization. A solution procedure for the model is suggested, but an efficient algorithm is not available for solving the model. Seme areas for future research are also suggested.
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