APPROXIMATE SOLUTIONS FOR CONTINUOUS-TIME QUADRATIC FRACTIONAL PROGRAMMING PROBLEMS

Abstract

In this article, a hybrid of the parametric method and discretization approach is proposed for a class of continuous-time quadratic fractional programming problems (CQFP). This approach leads to an approximation algorithm that solves the problem (CQFP) to any required accuracy. The analysis also shows that we can predetermine the size of discretization such that the accuracy of the corresponding approximate solution can be controlled within the predefined error tolerance. Hence, the trade-off between the quality of the results and the simplification of the problem can be controlled by the decision maker. Moreover, we prove the convergence of the searched sequence of approximate solutions.