1011 problems

Open problems

Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.

All fields Mathematics 97 Computer science 8 Physics & astronomy 1

Algorithms 2 Complexity 4 Computability 1 Optimisation 1

Source Any Curated here 2 Optimization constants 1

Verification Any A · Machine-checkable B · Reproducible C · Reviewed Tier Any Standard Hard Grand challenges

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B Optimisation · Optimization constants

Gradient Descent Exponent

Let f be a convex function with 1-Lipschitz gradient. We assume black-box access to the function and its gradient. Gradient descent will converge to a global minimum with an appropriate choice of _step size_ s: x_k+1 := x_k - s· ∇ f(x_k). In general, s can be chosen to vary with the step k.

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Gradient Descent Exponent

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