Simultaneous distributed-boundary optimal control problems driven by nonlinear complementarity systems

Jinxia Cen (), Tahar Haddad, Nguyen Van Thien () and Shengda Zeng ()
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Jinxia Cen: Yulin Normal University
Tahar Haddad: Université Mohammed Seddik Benyahia
Nguyen Van Thien: FPT University
Shengda Zeng: Yulin Normal University

Journal of Global Optimization, 2022, vol. 84, issue 3, No 10, 783-805

Abstract: Abstract The primary goal of this paper is to study a nonlinear complementarity system (NCS, for short) with a nonlinear and nonhomogeneous partial differential operator and mixed boundary conditions, and a simultaneous distributed-boundary optimal control problem governed by (NCS), respectively. First, we formulate the weak formulation of (NCS) to a mixed variational inequality with double obstacle constraints (MVI, for short), and prove the existence and uniqueness of solution to (MVI). Then, a power penalty method is applied to (NCS) for introducing an approximating mixed variational inequality without constraints (AMVI, for short). After that, a convergence result that the unique solution of (MVI) can be approached by the unique solution of (AMVI) when a penalty parameter tends to infinity, is established. Moreover, we explore the solvability of the simultaneous distributed-boundary optimal control problem described by (MVI), and consider a family of approximating optimal control problems driven by (AMVI). Finally, we provide a result on asymptotic behavior of optimal controls, system states and minimal values to approximating optimal control problems.

Keywords: Simultaneous optimal control problem; Mixed boundary condition; Complementarity problem; Nonhomogeneous partial differential operator; Asymptotic behavior; 49J20; 47J20; 49J40; 90C33; 35J25 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-022-01155-x

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