Mathematical Background to Dynamic Optimization

Abstract

This chapter starts with a brief description of solving time-continuous optimal control problems with pure state constraints analytically (Section 2.2). For a more detailed treatment of this type of problem, refer to Feichtinger & Hartl [1986]. Subsequently, discretization of time-continuous problems is explained so that numerically solving with the aid of a computer and specific programs for optimizing non-linear functions of a finite number of variables under nonlinear subsidiary conditions will be possible (Section 2.3). Then Section 2.4 gives a general economic interpretation of adjoint variables as shadow prices, both for continuous and discrete time problems. The last section deals with the procedure followed with the various models of the firm in this book.