scholarly journals Necessary and sufficient conditions for optimality for singular control problems: A limit approach

1971 ◽  
Vol 34 (2) ◽  
pp. 239-266 ◽  
Author(s):  
David H Jacobson ◽  
Jason L Speyer
Keyword(s):  
Sufficient Conditions ◽  
Singular Control ◽  
Necessary And Sufficient Conditions ◽  
Control Problems ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

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.

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

2014 ◽  
Vol 20 (3) ◽  
pp. 667-684 ◽  
Author(s):  
A. Kerem Coşar ◽  
Edward J. Green
Keyword(s):  
Optimization Problems ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Transversality Condition ◽  
Necessary And Sufficient Conditions ◽  
Infinite Horizon Optimization ◽  
Sufficient Conditions For Optimality ◽  
The Government ◽  
Duality Approach ◽  
Necessary And Sufficient

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

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