35 research outputs found
Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems
We consider optimal control problems with functional given by the ratio of
two integrals (fractional optimal control problems). In particular, we focus on a special
case with affine integrands and linear dynamics with respect to state and control.
Since the standard optimal control theory cannot be used directly to solve a problem
of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal
control problem can be transformed into an equivalent monoparametric family
{ P q } of linear optimal control problems. The special structure of the class of problems
considered allows solving the fractional problem either explicitly or requiring
straightforward classical numerical techniques to solve a single equation. An application
to advertising efficiency maximization is presented
On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program
summary:In this note we consider a linear-fractional programming problem with equality linear constraints. Following Rohn, we define a generalized relative sensitivity coefficient measuring the sensitivity of the optimal value for a linear program and a linear-fractional minimization problem with respect to the perturbations in the problem data.
By using an extension of Rohn's result for the linear programming case, we obtain, via Charnes-Cooper variable change, the relative sensitivity coefficient for the linear-fractional problem. This coefficient involves only the measure of data perturbation, the optimal solution for the initial linear-fractional problem and the optimal solution of the dual problem of linear programming equivalent to the initial fractional problem