An ellipsoid algorithm for equality-constrained nonlinear programs

This paper describes an ellipsoid algorithm that solves convex problems having linear equality constraints with or without inequality constraints. Experimental results show that the new method is also effective for some problems that have nonlinear equality constraints or are otherwise nonconvex. Th...

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Bibliographic Details
Published in:Computers & operations research 2001, Vol.28 (1), p.85-92
Main Authors: Shah, Sharmila, Mitchell, John E., Kupferschmid, Michael
Format: Article
Language:English
Subjects:
Algorithms
Ellipsoid algorithm
Equality constraints
Nonlinear optimization
Nonlinear programming
Optimization
Studies
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Summary:This paper describes an ellipsoid algorithm that solves convex problems having linear equality constraints with or without inequality constraints. Experimental results show that the new method is also effective for some problems that have nonlinear equality constraints or are otherwise nonconvex. The purpose of this paper is to present a variant of the ellipsoid algorithm that can be used with equalities. This is a significant improvement over the classical algorithm, which yields accurate solutions to convex and many nonconvex nonlinear programming problems but requires the feasible set to be of full dimension and therefore cannot be used with equality constraints.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/S0305-0548(99)00096-9