Using the Dinkelbach‐type algorithm to solve the continuous‐time linear fractional programming problems

A Dinkelbach‐type algorithm is proposed in this paper to solve a class of continuous‐time linear fractional programming problems. We shall transform this original problem into a continuous‐time non‐fractional programming problem, which unfortunately happens to be a continuous‐time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as parametric continuous‐time linear programming problem. We also introduce a dual problem of this parametric continuous‐time linear programming problem in which the weak duality theorem also holds true. We introduce the discrete approximation method to solve the primal and dual pair of parametric continuous‐time linear programming problems by using the recurrence method. Finally, we provide two numerical examples to demonstrate the usefulness of this practical algorithm.