A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

scholarly journals A general form of the weak maximum principle and some applications

2013 ◽  
Vol 29 (4) ◽  
pp. 1437-1476 ◽  
Author(s):  
Guglielmo Albanese ◽  
Luis Alías ◽  
Marco Rigoli
Keyword(s):  
Maximum Principle ◽  
Weak Maximum Principle

scholarly journals Maximum principle for non-linear degenerate equations of the parabolic type

1982 ◽  
Vol 25 (2) ◽  
pp. 251-263 ◽  
Author(s):  
Jan Chabrowski ◽  
Rudolf Výborný
Keyword(s):  
Maximum Principle ◽  
Differential Inequality ◽  
Parabolic Type ◽  
Degenerate Equations ◽  
Weak Maximum Principle ◽  
Degenerate Parabolic ◽  
The Difference ◽  
Image Position ◽  
Linear Degenerate ◽  
Nonlinear Degenerate

This paper establishes a weak maximum principle for the difference u − v of solutions to nonlinear degenerate parabolic differential inequality

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