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A Strengthened Conjecture on the Minimax Optimal Constant Stepsize for Gradient Descent
Benjamin Grimmer, Kevin Shu, Alex L. Wang
Drori and Teboulle [4] conjectured that the minimax optimal constant stepsize for N steps of gradient descent is given by the stepsize that balances performance on Huber and quadra…
Accelerated Objective Gap and Gradient Norm Convergence for Gradient Descent via Long Steps
Benjamin Grimmer, Kevin Shu, Alex L. Wang
This work considers gradient descent for L-smooth convex optimization with stepsizes larger than the classic regime where descent can be ensured. The stepsize schedules considered…
On semidefinite descriptions for convex hulls of quadratic programs
Alex L. Wang, Fatma Kilinc-Karzan
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural conv…
Accelerated Gradient Descent via Long Steps
Benjamin Grimmer, Kevin Shu, Alex L. Wang
Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps periodically, gradient descent's textbook convergence guarantees can be improved by c…
Implicit regularity and linear convergence rates for the generalized trust-region subproblem
Alex L. Wang, Yunlei Lu, Fatma Kilinc-Karzan
In this paper we develop efficient first-order algorithms for the generalized trust-region subproblem (GTRS), which has applications in signal processing, compressed sensing, and e…