Synthesis, Presynthesis, Sufficient Conditions for Optimality and Subanalytic Sets

2017 ◽  
pp. 1-19
Author(s):  
H. J. Sussmann
Keyword(s):  
Sufficient Conditions ◽  
Subanalytic Sets ◽  
Sufficient Conditions For Optimality

scholarly journals Invexity of supremum and infimum functions

2002 ◽  
Vol 65 (2) ◽  
pp. 289-306 ◽  
Author(s):  
Nguyen Xuan Ha ◽  
Do Van Luu
Keyword(s):  
Sufficient Conditions ◽  
Infinite Family ◽  
Lipschitz Functions ◽  
Necessary And Sufficient Conditions ◽  
Directional Derivatives ◽  
Mathematical Programs ◽  
Sufficient Conditions For Optimality ◽  
Invex Function ◽  
Necessary And Sufficient

Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or infimum are an invex function when all functions of the invex. Applying these results to a class of mathematical programs, we obtain necessary and sufficient conditions for optimality.

On the optimal control of a deterministic epidemic

1974 ◽  
Vol 6 (04) ◽  
pp. 622-635 ◽  
Author(s):  
R. Morton ◽  
K. H. Wickwire
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Sufficient Conditions ◽  
Bounded Control ◽  
Closed Population ◽  
Control Scheme ◽  
Optimal Policies ◽  
Sufficient Conditions For Optimality ◽  
The Cost ◽  
Cost Functionals

A control scheme for the immunisation of susceptibles in the Kermack-McKendrick epidemic model for a closed population is proposed. The bounded control appears linearly in both dynamics and integral cost functionals and any optimal policies are of the “bang-bang” type. The approach uses Dynamic Programming and Pontryagin's Maximum Principle and allows one, for certain values of the cost and removal rates, to apply necessary and sufficient conditions for optimality and show that a one-switch candidate is the optimal control. In the remaining cases we are still able to show that an optimal control, if it exists, has at most one switch.

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