7 papers
Optimal Nonergodic Primal-Dual Complexity of Efficient Inexact Parameter-Free Augmented Lagrangian Methods
Arnesh Sujanani, Saeed Ghadimi, Henry Wołkowicz
Augmented Lagrangian (AL) methods are a classical framework for constrained optimization, but for directly verifiable approximate KKT points, known first-order complexity bounds fo…
Optimal Diagonal Preconditioning Beyond Worst-Case Conditioning: Theory and Practice of Omega Scaling
Saeed Ghadimi, Woosuk L. Jung, Arnesh Sujanani +2
We study optimal diagonal preconditioning using the classical worst-case -condition number and the averaging-based -condition number. For the -optimal preconditioning prob…
A User Manual for cuHALLaR: A GPU Accelerated Low-Rank Semidefinite Programming Solver
Jacob Aguirre, Diego Cifuentes, Vincent Guigues +3
We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numericall…
cuHALLaR: A GPU Accelerated Low-Rank Augmented Lagrangian Method for Large-Scale Semidefinite Programming
Jacob M. Aguirre, Diego Cifuentes, Vincent Guigues +3
This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) proble…
Efficient parameter-free restarted accelerated gradient methods for convex and strongly convex optimization
Arnesh Sujanani, Renato D. C. Monteiro
This paper develops a new parameter-free restarted method, namely RPF-SFISTA, and a new parameter-free aggressive regularization method, namely A-REG, for solving strongly convex a…
A low-rank augmented Lagrangian method for large-scale semidefinite programming based on a hybrid convex-nonconvex approach
Renato D. C. Monteiro, Arnesh Sujanani, Diego Cifuentes
This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) meth…
An adaptive superfast inexact proximal augmented Lagrangian method for smooth nonconvex composite optimization problems
Arnesh Sujanani, Renato D. C. Monteiro
This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each itera…