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A New Perspective of Accelerated Gradient Methods: The Controlled Invariant Manifold Approach (2305.10756v3)

Published 18 May 2023 in math.OC

Abstract: Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x*}$ of the optimization problem must be attained in a minimum number of iterations. For this objective, the paper proposes a genesis of an accelerated gradient algorithm through the controlled dynamical system perspective. The objective of optimally reaching the optimal solution $\mathrm{x*}$ where $\mathrm{\nabla f(x*)=0}$ with a given initial condition $\mathrm{x(0)}$ is achieved through control.

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