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Saddle‐point optimality criteria in modified variational control problems with partial differential equation constraints
Author(s) -
Treanţă Savin
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2594
Subject(s) - saddle point , convexity , mathematics , lagrange multiplier , equivalence (formal languages) , partial differential equation , variational analysis , mathematical optimization , optimal control , variational inequality , partial derivative , calculus of variations , saddle , mathematical analysis , pure mathematics , geometry , financial economics , economics
Summary In this article, based on a multidimensional control problem, in short ( MCP ), we introduce a modified multidimensional variational control problem involving first‐order partial differential equations and inequality‐type constraints. As well, we formulate and prove optimality conditions for this new variational control problem. Furthermore, we establish (under some generalized convexity assumptions) an equivalence between an optimal solution of ( MCP ) and a saddle‐point associated with the Lagrange functional (Lagrangian) corresponding to the modified multidimensional control problem. Also, in order to illustrate our main characterization results and their effectiveness, we present several applications.