Turnpike property of optimal solutions of infinite-horizon variational problems

2002 ◽  
Author(s):  
A.J. Zaslavski
Keyword(s):  
Infinite Horizon ◽  
Variational Problems ◽  
Optimal Solutions ◽  
Turnpike Property

scholarly journals Existence and uniform boundedness of optimal solutions of variational problems

1998 ◽  
Vol 3 (3-4) ◽  
pp. 265-292 ◽  
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Minimization Problem ◽  
Infinite Horizon ◽  
Uniform Boundedness ◽  
Approximate Solutions ◽  
Variational Problems ◽  
Initial Condition ◽  
Optimal Solutions ◽  
Initial Value ◽  
Horizon Problem ◽  
Bounded Set

Given anx0∈Rnwe study the infinite horizon problem of minimizing the expression∫0Tf(t,x(t),x′(t))dtasTgrows to infinity wherex:[0,∞)→Rnsatisfies the initial conditionx(0)=x0. We analyse the existence and the properties of approximate solutions for every prescribed initial valuex0. We also establish that for every bounded setE⊂RntheC([0,T])norms of approximate solutionsx:[0,T]→Rnfor the minimization problem on an interval[0,T]withx(0),x(T)∈Eare bounded by some constant which does not depend onT.

INFLUENCE OF INVESTING IN TREATING A POLLUTED ENVIRONMENT ON THE HARVEST: A PROBLEM OF OPTIMAL ALLOCATION

2019 ◽  
Vol 27 (02) ◽  
pp. 257-279
Author(s):  
P. D. N. SRINIVASU ◽  
SIMON D. ZAWKA
Keyword(s):  
Optimal Allocation ◽  
Infinite Horizon ◽  
Renewable Resource ◽  
Maximum Sustainable Yield ◽  
Allocation Problem ◽  
Sustainable Yield ◽  
Optimal Solutions ◽  
Polluted Environment ◽  
Sole Owner

This study is concerned with harvesting a renewable resource that is surviving in a polluted environment. Fall in the revenue from the resource due to presence of pollution in the environment drives the sole owner to allocate a part of the available effort towards treating the environment and the interest is to find the optimal allocation of the available effort towards harvesting the resource and treating the environment so that the revenue is maximized. Resource-pollution dynamics are studied, maximum sustainable yield and maximum sustainable revenue have been evaluated. Further, an optimal allocation problem has been formulated on infinite horizon and optimal solutions are obtained. Key results of the study are demonstrated through numerical illustrations.

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