Publication: An augmented Lagrangian interior-point method using directions of negative curvature
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2003-03
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Springer
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Abstract
We describe an efficient implementation of an interior-point algorithm for non-convex problems
that uses directions of negative curvature. These directions should ensure convergence to second-order KKT
points and improve the computational efficiency of the procedure. Some relevant aspects of the implementation
are the strategy to combine a direction of negative curvature and a modified Newton direction, and
the conditions to ensure feasibility of the iterates with respect to the simple bounds. The use of multivariate
barrier and penalty parameters is also discussed, as well as the update rules for these parameters.We analyze
the convergence of the procedure; both the linesearch and the update rule for the barrier parameter behave
appropriately. As the main goal of the paper is the practical usage of negative curvature, a set of numerical
results on small test problems is presented. Based on these results, the relevance of using directions of negative
curvature is discussed.
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The original publication is available at www.springerlink.com
Keywords
Primal-dual methods, Nonconvex optimization, Linesearches, 49M37, 65K05, 90C30
Bibliographic citation
Mathematical Programming, 2003, vol. 95, no. 3, pp. 573-616.