Constrained optimization methods in Hilbert spaces and their applications to optimal control problems with functional inequality constraints

1986 ◽  
Vol 31 (6) ◽  
pp. 559-564 ◽  
Author(s):  
K. Shimizu ◽  
S. Fujimaki ◽  
Yo Ishizuka
Keyword(s):  
Optimal Control ◽  
Constrained Optimization ◽  
Hilbert Spaces ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Optimization Methods ◽  
Functional Inequality ◽  
Control Problems

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.

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