Projected Subgradient Ascent for Convex Maximization

Pedro Felzenszwalb; Heon Lee

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arXiv · 2511.00741

Projected Subgradient Ascent for Convex Maximization

Pedro Felzenszwalb·Heon Lee

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Abstract

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex functions over convex sets, we show that projected subgradient ascent converges to a first-order stationary point when using arbitrarily large step sizes. Taking the step sizes to infinity leads to a deterministic variant of the conditional gradient algorithm, and iterated linear optimization as a special case.

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Pedro Felzenszwalb, Heon Lee. 2025-11-01. Projected Subgradient Ascent for Convex Maximization. https://arxiv.org/abs/2511.00741

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