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An Efficient Nonmonotone Method for State-Constrained Elliptic Optimal Control Problems

  • Omid Solaymani FardEmail author
  • Farhad Sarani
  • Hadi Nosratipour
Original Paper
  • 31 Downloads

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 

Mathematics Subject Classification

49K20 65N06 90C30 

Notes

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran
  2. 2.School of Mathematics and Computer ScienceDamghan UniversityDamghanIran
  3. 3.Department of Mathematics, Faculty of ScienceRazi UniversityKermanshahIran

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