Optimal multi-therapeutic HIV treatment using a global optimal switching scheme

The problem of multi-therapeutic HIV treatment is posed in this study as a switching problem to find the optimal switching time between the different therapies. To solve the optimal switching problem with nonlinear subsystems an algorithm is developed for learning the cost-to-go as a function versus different switching times and different initial conditions. Once the function is obtained in a closed form, finding optimal switching time for every given initial condition reduces to a function optimization. Through numerical simulations of a model for the HIV problem, the proposed algorithm is shown to be a useful tool for solving this class of problems.