Optimal Control of an Evolution Problem Involving Time-Dependent Maximal Monotone Operators

Nesrine Bouhali, Dalila Azzam-Laouir () and Manuel D. P. Monteiro Marques ()
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Nesrine Bouhali: Université Mohammed Seddik Benyahia
Dalila Azzam-Laouir: Université Mohammed Seddik Benyahia
Manuel D. P. Monteiro Marques: Faculdade de Ciências da Universidade de Lisboa

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 1, No 3, 59-91

Abstract: Abstract We consider a control problem in a finite-dimensional setting, which consists in finding a minimizer for a standard functional defined by way of two continuous and bounded below functions and a convex function, where the control functions take values in a closed convex set and the state functions solve a differential system made up of a differential inclusion governed by a maximal monotone operator; and an ordinary differential equation with a Lipschitz mapping in the right-hand side. We first show the existence of a unique absolutely continuous solution of our system, by transforming it to a sole evolution differential inclusion, and then use a result from the literature. Secondly, we prove the existence of an optimal solution to our problem. The main novelties are: the presence of the time-dependent maximal monotone operators, which may depend as well as their domains on the time variable; and the discretization scheme for the approximation of the solution.

Keywords: Absolutely continuous variation; Maximal monotone operator; Objective function; Optimal solution; Pseudo-distance; 49J21; 34H05; 49J15; 93C15; 34A60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02009-y

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