Inexact restoration for derivative-free expensive function minimization and applications
Birgin, E. . G. 1Krejic, N. 2Martinez, J. . M.3
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作者信息
1. Univ Sao Paulo
2. Univ Novi Sad
3. Univ Estadual Campinas
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Abstract
The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision. This framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low-and high-precision evaluations. In this paper we consider the case where the domain of the optimization problem is an abstract metric space. Assumptions about differentiability or even continuity will not be used in the general algorithm based on Inexact Restoration. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A new derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that takes advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier