Frictionless Hamiltonian Descent and Coordinate Hamiltonian Descent for Strongly Convex Quadratic Problems

Jun-Kun Wang

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arXiv · 2402.13988

Frictionless Hamiltonian Descent and Coordinate Hamiltonian Descent for Strongly Convex Quadratic Problems

Jun-Kun Wang

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Abstract

We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic functions and show that the method has a non-trivial accelerated rate as that of Heavy Ball flow. We also propose Frictionless Coordinate Hamiltonian Descent and its parallelizable variant, which turns out to encapsulate the classical Gauss-Seidel method, Successive Over-relaxation, Jacobi method, and more, for solving a linear system of equations. The result not only offers a new perspective on these existing algorithms but also leads to a broader class of update schemes that guarantee the convergence.

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Jun-Kun Wang. 2024-02-21. Frictionless Hamiltonian Descent and Coordinate Hamiltonian Descent for Strongly Convex Quadratic Problems. https://arxiv.org/abs/2402.13988

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