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A duality theory for infinite-horizon optimization of concave input/output processes. (English) Zbl 0532.90021

Summary: A general concave \(\infty\)-horizon optimization model is analyzed with the help of a special convexity concept, which combines both the usual convexity and the dynamic structure. The axiomatic setup leads to a perfect symmetry between the primal and dual problems. After introducing a particular dynamic feasibility hypothesis, the following results are presented: (i) boundedness of trajectories as a necessary condition for optimality, (ii) the existence of primal and dual optimal trajectories, (iii) approximation by finite horizon models, and (iv) necessary and sufficient conditions for optimality.

MSC:

91B62 Economic growth models
90C90 Applications of mathematical programming
49N15 Duality theory (optimization)
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