Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence

Kiyuob Jung; Jehan Oh

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arXiv · 2412.20747

Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence

Kiyuob Jung·Jehan Oh

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Abstract

We propose the specular gradient method for one-dimensional convex optimization. Assuming that the minimum is attained and a suitable initial distance bound holds, we establish R-linear convergence using normalized steps of geometrically decreasing length. Neither strong convexity nor differentiability is required.

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Kiyuob Jung, Jehan Oh. 2024-12-30. Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence. https://arxiv.org/abs/2412.20747

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