A class of linear quadratic dynamic optimization problems with state dependent constraints

Rajani Singh () and Agnieszka Wiszniewska-Matyszkiel
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Rajani Singh: University of Warsaw

Mathematical Methods of Operations Research, 2020, vol. 91, issue 2, No 7, 325-355

Abstract: Abstract In this paper, we analyse a wide class of discrete time one-dimensional dynamic optimization problems—with strictly concave current payoffs and linear state dependent constraints on the control parameter as well as non-negativity constraint on the state variable and control. This model suits well economic problems like extraction of a renewable resource (e.g. a fishery or forest harvesting). The class of sub-problems considered encompasses a linear quadratic optimal control problem as well as models with maximal carrying capacity of the environment (saturation). This problem is also interesting from theoretical point of view—although it seems simple in its linear quadratic form, calculation of the optimal control is nontrivial because of constraints and the solutions has a complicated form. We consider both the infinite time horizon problem and its finite horizon truncations.

Keywords: Bellman equation; Constraints; State dependent constraints; State constraints; Linear quadratic optimal control problem; Renewable resources; Carrying capacity; 90C39; 49L20; 91B76; 91B32 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-019-00688-4

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