The High-Order Maximum Principle: From Approximations of Reachable Sets to High-Order Necessary Conditions for Optimality

2012 ◽  
pp. 231-321
Author(s):  
Heinz Schättler ◽  
Urszula Ledzewicz
Keyword(s):  
Maximum Principle ◽  
Necessary Conditions ◽  
High Order ◽  
Reachable Sets ◽  
Necessary Conditions For Optimality

scholarly journals Maximum principle for a nonlinear size-structured model of fish and fry management

2018 ◽  
Vol 23 (4) ◽  
pp. 533-552 ◽  
Author(s):  
Rong Liu ◽  
Guirong Liu
Keyword(s):  
Fixed Point ◽  
Maximum Principle ◽  
Normal Cone ◽  
Necessary Conditions ◽  
Adjoint System ◽  
Banach Fixed Point Theorem ◽  
Structured Model ◽  
The Maximum Principle ◽  
Necessary Conditions For Optimality ◽  
Theoretical Results

This paper investigates the maximum principle for a nonlinear size-structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. We establish the well-posedness of the state system by Banach fixed-point theorem. Necessary conditions for optimality are established via the normal cone technique and adjoint system. The existence of a unique optimal policy is proved via Ekeland's variational principle and fixed-point reasoning. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper.

High Order Necessary Conditions for Optimality

1972 ◽  
Vol 10 (1) ◽  
pp. 127-168 ◽  
Author(s):  
R. Gabasov ◽  
F. M. Kirillova
Keyword(s):  
Necessary Conditions ◽  
High Order ◽  
Necessary Conditions For Optimality

scholarly journals High-order optimality conditions for degenerate variational problems

2014 ◽  
Vol 30 (3) ◽  
pp. 387-394
Author(s):  
AGNIESZKA PRUSINSKA ◽  
◽  
EWA SZCZEPANIK ◽  
ALEXEY A. TRETYAKOV ◽  
◽  
...  
Keyword(s):  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Necessary Conditions ◽  
Regularity Theory ◽  
Variational Problems ◽  
High Order ◽  
Singular Problems ◽  
Necessary Conditions For Optimality ◽  
Solution Point

The paper is devoted to the class of singular calculus of variations problems with constraints which are not regular mappings at the solution point. Methods of the p-regularity theory are used for investigation of isoperimetric and Lagrange singular problems. Necessary conditions for optimality in p-regular calculus of variations problem are presented.

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