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math.OC2023★ 8 cited
Acceleration by Stepsize Hedging II: Silver Stepsize Schedule for Smooth Convex Optimization
Jason M. Altschuler, Pablo A. Parrilo
We provide a concise, self-contained proof that the Silver Stepsize Schedule proposed in Part I directly applies to smooth (non-strongly) convex optimization. Specifically, we show…
math.OC2023
Improved Nonnegativity Testing in the Bernstein Basis via Geometric Means
Mitchell Tong Harris, Pablo A. Parrilo
We develop a new kind of nonnegativity certificate for univariate polynomials on an interval. In many applications, nonnegative Bernstein coefficients are often used as a simple wa…
math.OC2023★ 6 cited
Acceleration by Stepsize Hedging I: Multi-Step Descent and the Silver Stepsize Schedule
Jason M. Altschuler, Pablo A. Parrilo
Can we accelerate convergence of gradient descent without changing the algorithm -- just by carefully choosing stepsizes? Surprisingly, we show that the answer is yes. Our proposed…