Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty
For practitioners needing to solve convex optimization problems with uncertainty and many variables, this work offers a practical algorithm, though it is incremental and lacks theoretical guarantees on sample complexity.
The paper proposes sequential randomized algorithms for convex optimization under uncertainty, enabling application to problems with many design variables. Numerical simulations on hard-disk drive servo design demonstrate effectiveness, though no a priori sample complexity bounds are provided.
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.