On a modified optimal control problem with first-order PDE constraints and the associated saddle-point optimality criterion

In this paper, based on a new multidimensional optimal control problem, in short (OCP), we introduce a modified multidimensional optimal control problem (which is simpler or easier to solve than the original one) involving first-order partial differential equations (PDEs) and inequality-type constra...

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Bibliographic Details
Published inEuropean journal of control Vol. 51; pp. 1 - 9
Main Author Treanţă, Savin
Format Journal Article
LanguageEnglish
Published Philadelphia Elsevier Ltd 01.01.2020
Elsevier Limited
Subjects
Convexity
Generalized convexity
Inventory management
Optimal control
Optimality criteria
Optimization
Partial differential equations
Saddle points
Saddle-point
Simulation
Saddle-point
90C30
49K20
Optimal control
46T20
65K10
26B25
Generalized convexity
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Summary:In this paper, based on a new multidimensional optimal control problem, in short (OCP), we introduce a modified multidimensional optimal control problem (which is simpler or easier to solve than the original one) involving first-order partial differential equations (PDEs) and inequality-type constraints. Optimality conditions associated with this new optimal control problem are formulated and proved, as well. Furthermore, under some generalized convexity assumptions, we establish an equivalence between an optimal solution of (OCP) and a saddle-point associated with the Lagrange functional corresponding to the modified multidimensional optimal control problem. Also, in order to illustrate the main results and their effectiveness, some applications are presented.
ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2019.07.003