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A New Perspective of Accelerated Gradient Methods: The Controlled Invariant Manifold Approach
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  • Revati Gunjal ,
  • Sushama Wagh ,
  • Syed Shadab Nayeer ,
  • A. M. Stankovic ,
  • Navdeep Singh
Revati Gunjal
Veermata Jijabai Technological Institute, Veermata Jijabai Technological Institute

Corresponding Author:[email protected]

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Sushama Wagh
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Syed Shadab Nayeer
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A. M. Stankovic
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Navdeep Singh
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Abstract

Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution 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 x* where the gradient of  ∇f(x*) is zero with a given initial condition x(0) is achieved through control.