Optimal control of a growth/consumption model

Abstract

This article concerns an optimal control problem arising in neo-classical macro-economics, where the objective is to maximize expenditure on social programs over the time horizon by choosing the appropriate balance between investment for growth and consumption. The underlying model and utility function are due to Solow and have their origins in a planning problem studied by Ramsey. The problem is of control theoretic interest, because the right side of the controlled differential equation and also the utility integrand are not uniformly Lipschitz continuous with respect to the state variable, owing to the presence of a fractional singularity. We introduce and apply a nonstandard verification technique, the verification function for which has infinite slope at a point approaching the boundary of its domain, to deal with these singularities and to provide a detailed solution to the problem and analyze its structure, for arbitrary initial data.

High-level simulation model of tourism industry dynamics

“…Each region is unique in its way, and it is necessary to provide investment support by their characteristics [9]. Such important management decisions cannot be made without full information and analytical support, which can be provided by the domestic tourism model and the data model, respectively [10,11].…”