7 papers
Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth
Zhenwei Lin, Zhe Zhang
We study why the proximal bundle method (PBM) can perform better in practice when it retains more cutting planes. We consider convex objectives with quadratic growth and an unknown…
Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization II: Function-constrained Optimization
Zhenwei Lin, Zhenewei Lin, Zhe Zhang
We introduce an anytime, almost parameter-free algorithm for convex function-constrained optimization, in which the objective and constraint functions are unknown piecewise-smooth.…
Optimal Parameter-Free First-Order Methods for Convex Optimization with Unknown Growth and Smoothness
Liwei Jiang, Ke Tang, Zhe Zhang
We study deterministic first-order minimization of a convex function without prior knowledge of the objective's growth, smoothness regime, or associated parameters. We develop anyt…
Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization I: Convex Optimization
Zhenwei Lin, Zhe Zhang
We introduce a nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic-growth (QG) condition, where the locations and structure o…
Linearly Convergent Algorithms for Nonsmooth Problems with Unknown Smooth Regions
Zhe Zhang, Suvrit Sra
We develop efficient algorithms for optimizing piecewise smooth (PWS) functions when their smooth regions are \emph{unknown} to the algorithm. For convex PWS functions satisfying a…
A Non-Asymptotic Theory of Seminorm Lyapunov Stability: From Deterministic to Stochastic Iterative Algorithms
Zaiwei Chen, Sheng Zhang, Zhe Zhang +2
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms i…
First-Order Methods for Linearly Constrained Bilevel Optimization
Guy Kornowski, Swati Padmanabhan, Kai Wang +2
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained b…