A linear programming-based optimization algorithm for solving nonlinear programming problems

In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush–Kuhn–Tucker stationary point is proved and numerical experience on some well-known test sets is showed...

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Bibliographic Details
Published in:European journal of operational research Vol. 200; no. 3; pp. 658 - 670
Main Authors: Still, Claus, Westerlund, Tapio
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.02.2010
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Cutting plane algorithms
Cutting stock problem
Exact sciences and technology
Linear programming
Mathematical programming
Nonlinear programming
Nonlinear programming Cutting plane algorithms Sequential linear programming
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Sequential linear programming
Studies
Sequential linear programming
Cutting plane algorithms
Nonlinear programming
Lower bound
Tree(graph)
Branch and bound method
Linear programming
Mixed integer programming
Non linear programming
Cutting plane method
Convex programming
Competitive algorithms
Bounded solution
Stationary condition
Sequential method
Karush Kuhn Tucker method
Inequality constraint
Equality constraint
Problem solving
Alternative method
ISSN:0377-2217, 1872-6860
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Summary:In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush–Kuhn–Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2009.01.033