AN INTERVAL-TYPE ALGORITHM FOR CONTINUOUS-TIME LINEAR FRACTIONAL PROGRAMMING PROBLEMS

Abstract

An interval-type computational procedure by combining the parametric method and discretization approach is proposed in this paper to solve a class of continuous-time linear fractional programming problems (CLFP). Using the different step sizes of discretization problems, we construct a sequence of convex, piecewise linear and strictly decreasing upper and lower bound functions. The zeros of upper and lower bound functions then determine a sequence of intervals shrinking to the optimal value of (CLFP) as the size of discretization getting larger. By using the intervals we can find corresponding approximate solutions to (CLFP). We also establish upper bounds of lengths of these intervals, and thereby we can determine the size of discretization in advance such that the accuracy of the corresponding approximate solution can be controlled within the predefined error tolerance. Moreover, we prove that the searched sequence of approximate solution functions weakly-star converges to an optimal solution of (CLFP). Finally, we provide some numerical examples to implement our proposed method.