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There is a growing interest in using robust control theory to analyze anddesign optimization and machine learning algorithms. This paper studies a classof nonconvex optimization problems whose cost functions satisfy the so-calledRegularity Condition (RC). Empirical studies show that accelerated gradientdescent (AGD) algorithms (e.g. Nesterov's acceleration and Heavy-ball) withproper initializations often work well in practice. However, the convergence ofsuch AGD algorithms is largely unknown in the literature. The main contributionof this paper is the analytical characterization of the convergence regions ofAGD under RC via robust control tools. Since such optimization problems arisefrequently in many applications such as phase retrieval, training of neuralnetworks and matrix sensing, our result shows promise of robust control theoryin these areas.

Analytical Convergence Regions of Accelerated Gradient Descent in Nonconvex Optimization under Regularity Condition