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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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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Abstract	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.
AbstractList	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. [PUBLICATION ABSTRACT] 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.
Author	Still, Claus Westerlund, Tapio
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Keywords	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
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SubjectTerms	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
Title	A linear programming-based optimization algorithm for solving nonlinear programming problems
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