Error estimation in nonlinear optimization

William Hager () and Delphine Mico-Umutesi ()
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William Hager: http://people.clas.ufl.edu/hager/

Journal of Global Optimization, 2014, vol. 59, issue 2, 327-341

Abstract: Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality conditions hold. A second estimate, based on the solution of an unconstrained nonconvex, nonsmooth optimization problem, is valid even when strict complementary slackness is violated. Both estimates are valid in a neighborhood of a local minimizer. An active set algorithm is developed for computing a stationary point of the nonsmooth error estimator. Each iteration of the algorithm requires the solution of a symmetric, positive semidefinite linear system, followed by a line search. Convergence is achieved in a finite number of iterations. The error bounds are based on stability properties for nonlinear programs. The theory is illustrated by some numerical examples. Copyright Springer Science+Business Media New York 2014

Keywords: Error bounds; KKT conditions; Active set algorithm; Nonconvex quadratic programming; Nonlinear programming (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-014-0186-y

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