Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

TL;DR

This paper introduces new sequential randomized algorithms for convex optimization under uncertainty, expanding their applicability to complex real-world problems with many variables, supported by theoretical analysis and numerical simulations.

Contribution

The paper presents novel sequential randomized algorithms with rigorous analysis for convex optimization under uncertainty, applicable to large-scale problems without requiring prior sample complexity bounds.

Findings

Algorithms successfully handle large numbers of design variables.

Theoretical guarantees for full and partial constraint satisfaction.

Numerical simulations demonstrate practical effectiveness in hard-disk drive design.

Abstract

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.