A New Perspective of Accelerated Gradient Methods: The Controlled Invariant Manifold Approach Article Swipe

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Revati Gunjal , Sushama Wagh , Syed Shadab Nayeer , A.M. Stanković , Navdeep Singh ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.36227/techrxiv.22964333.v2

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.

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Gradient Descent

Mathematics

Optimal Control

Perspective (Graphical)

Artificial Intelligence

Engineering

Mechanical Engineering

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Gradient descent Mathematics Gradient method Optimal control Invariant (physics) Perspective (graphical) Manifold (fluid mechanics) Optimization problem Applied mathematics Mathematical optimization Control theory (sociology) Combinatorics Computer science Control (management) Mathematical physics Geometry Artificial neural network Artificial intelligence Engineering Mechanical engineering

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Type: preprint
Language: en
Landing Page: https://doi.org/10.36227/techrxiv.22964333.v2
PDF: https://www.techrxiv.org/articles/preprint/A_New_Perspective_of_Accelerated_Gradient_Methods_The_Controlled_Invariant_Manifold_Approach/22964333/2/files/40985405.pdf
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Cited By: 3
References: 31
Related Works: 10
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DOI: https://doi.org/10.36227/techrxiv.22964333.v2

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Title: A New Perspective of Accelerated Gradient Methods: The Controlled Invariant Manifold Approach

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Language: en

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Publication year: 2023

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Publication date: 2023-05-31

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Authors: Revati Gunjal, Sushama Wagh, Syed Shadab Nayeer, A.M. Stanković, Navdeep Singh

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Landing page: https://doi.org/10.36227/techrxiv.22964333.v2

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Concepts: Gradient descent, Mathematics, Gradient method, Optimal control, Invariant (physics), Perspective (graphical), Manifold (fluid mechanics), Optimization problem, Applied mathematics, Mathematical optimization, Control theory (sociology), Combinatorics, Computer science, Control (management), Mathematical physics, Geometry, Artificial neural network, Artificial intelligence, Engineering, Mechanical engineering

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Cited by: 3

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Citations by year (recent): 2024: 2, 2023: 1

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