New general analytic and numerical methods in constrained optimization with applications to optimal consumption
Abstract
New analytic methods are given to solve general economic models which occur as constrained optimization problems in the calculus of variation or optimal control theory. These methods allow us to solve problems including equality and inequality differential and integral constraints with a complete variety of endpoint conditions. They also allow us to determine the multipliers or shadow variables. For economic problems which do not yield closed formed solutions general, accurate and efficient numerical methods, which go with these analytic methods, given by the first author are available. These methods have pointwise, maximum, numerical errors proportional to h2 where h is the discretization step size. These new methods are applied to a general optimal consumption model and then used to solve this model. A specific example of this model is also considered.
