PDA-Based Method for Convex Optimization

Abstract

In this chapter we use predicted decrease approximation (PDA) for constrained convex optimization. For PDA-based method each iteration consists of two steps. In each of these two steps there is a computational error. In general, these two computational errors are different. We show that our algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if we know the computational errors for the two steps of our algorithm, we find out what approximate solution can be obtained and how many iterates one needs for this.