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Error estimation in nonlinear optimization

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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

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  • William Hager & Delphine Mico-Umutesi, 2014. "Error estimation in nonlinear optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 327-341, July.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:2:p:327-341
    DOI: 10.1007/s10898-014-0186-y
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    1. Joydeep Dutta & Kalyanmoy Deb & Rupesh Tulshyan & Ramnik Arora, 2013. "Approximate KKT points and a proximity measure for termination," Journal of Global Optimization, Springer, vol. 56(4), pages 1463-1499, August.
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