SOLVING A CLASS OF CONTINUOUS-TIME CONVEX PROGRAMMING PROBLEMS WITH APPROXIMATION

This article is focused on an approximate solution method for a class of continuous-time convex programming problems (CCP). A discrete approximation algorithm is developed to solve the problems (CCP). The estimate for the size of discretization and the error bound of approximate solutions are also established. Especially, we can predetermine the size of discretization such that the accuracy of the corresponding approximate solution can be controlled within the predefined error tolerance. In addition, it can be shown that the searched sequence of approximate solution functions weakly-star converges to an optimal solution of (CCP). Finally, some numerical examples are provided to implement the proposed method.