Yu. P. Yatsenko

Optimal control of Solow vintage capital model with nonlinear utility

An optimization problem with nonlinear utility is investigated in the well-known Ramsey vintage capital model described by nonlinear Volterra integral equations with an unknown function in the lower integration limits. The necessary and sufficient condition for an extremum is proven and a qualitative analysis is provided. A balanced growth case is found and a turnpike theorem is established for this problem. The obtained results demonstrate new phenomena as compared with the case of the linear utility optimization.

Optimization in integral model of develops systems

The paper deals with one optimal control problem for integral dynamical model with unknowns in lower integral limits. The structure and asymptotic behaviour of optimal model trajectories are studied, especially the turn-pike properties are established.