Bulletin of the Iranian Mathematical Society, Volume (46), No (4), Year (2019-10) , Pages (943-963)

Title : ( An Efficient Nonmonotone Method for State-Constrained Elliptic Optimal Control Problems )

Authors: Omid Solaymani Fard , Farhad Sarani , Hadi Nosratipour ,

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Abstract

This paper presents a novel numerical strategy based on combination of an adaptive semismooth Newton (ASN) method and the Lavrentiev regularization technique for the solution of elliptic optimal control problems with state constraints. Using the global convergence proof for a nonmonotone semismooth Newton method, we will exploit an adaptive nonmonotone line search method such that the nonmonotonicity degree of this method can be increased when the results are far from the optimum solution and it can be reduced when they are close to the optimizer. In this strategy, the role of the Lavrentiev regularization technique is converting the original optimal control problem to a regularized optimal control problem. Using the finite difference discretization scheme and a Newton–Cotes rule, the regularized optimal control problem is converted to a bound constrained optimization problem (BCOP). Then the ASN method is implemented to solve the resulting BCOP. Numerical results show the efficiency of the proposed procedure.

Keywords

, Optimal control, Nonmonotone semismooth Newton method, State constraints, Finite difference discretization scheme
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@article{paperid:1080099,
author = {Solaymani Fard, Omid and فرهاد سارانی and هادی نصرتی پور},
title = {An Efficient Nonmonotone Method for State-Constrained Elliptic Optimal Control Problems},
journal = {Bulletin of the Iranian Mathematical Society},
year = {2019},
volume = {46},
number = {4},
month = {October},
issn = {1735-8515},
pages = {943--963},
numpages = {20},
keywords = {Optimal control; Nonmonotone semismooth Newton method; State constraints; Finite difference discretization scheme},
}

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%0 Journal Article
%T An Efficient Nonmonotone Method for State-Constrained Elliptic Optimal Control Problems
%A Solaymani Fard, Omid
%A فرهاد سارانی
%A هادی نصرتی پور
%J Bulletin of the Iranian Mathematical Society
%@ 1735-8515
%D 2019

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