A new relaxation method for optimal control of semilinear elliptic variational inequalities obstacle problems | Zendy

El Hassene Osmani | Zendy; Mounir Haddou | Zendy; Naceurdine Bensalem | Zendy

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A new relaxation method for optimal control of semilinear elliptic variational inequalities obstacle problems

Author(s) -

El Hassene Osmani,

Mounir Haddou,

Naceurdine Bensalem

Publication year - 2021

Publication title -

numerical algebra control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.303

H-Index - 20

eISSN - 2155-3289

pISSN - 2155-3297

DOI - 10.3934/naco.2021061

Subject(s) - variational inequality , obstacle , lagrange multiplier , interior point method , mathematics , obstacle problem , mathematical optimization , optimal control , relaxation (psychology) , domain (mathematical analysis) , nonlinear programming , point (geometry) , nonlinear system , quadratic equation , optimization problem , quadratic programming , mathematical analysis , psychology , social psychology , physics , geometry , quantum mechanics , political science , law

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using the Interior Point Optimizer (IPOPT), Nonlinear Interior point Trust Region Optimization (KNITRO) and Sequential Quadratic Optimization Technique (SNOPT) are presented to verify the efficiency of our approach.

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