5 papers
An Adaptive Smoothing Algorithm for Non-Lipschitz Optimization on Manifolds with Complexity Guarantees
Lei Wang, Xiaojun Chen
We study a class of optimization problems on Riemannian manifolds, where the objective function consists of a smooth term and quasi-norm type penalties with exponent …
Complexity of Projected Gradient Methods for Strongly Convex Optimization with Hölder Continuous Gradient Terms
Xiaojun Chen, C. T. Kelley, Lei Wang
This paper studies the complexity of projected gradient descent methods for a class of strongly convex constrained optimization problems where the objective function is expressed a…
A Support-Set Algorithm for Optimization Problems with Nonnegative and Orthogonal Constraints
Lei Wang, Xin Liu, Xiaojun Chen
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size exhibits a sparsity pattern such tha…
Enhancing Distributional Robustness in Principal Component Analysis by Wasserstein Distances
Lei Wang, Xin Liu, Xiaojun Chen
We consider the distributionally robust optimization (DRO) model of principal component analysis (PCA) to account for uncertainty in the underlying probability distribution. The re…
A New Complexity Result for Strongly Convex Optimization with Locally -H{ö}lder Continuous Gradients
Xiaojun Chen, C. T. Kelley, Lei Wang
In this paper, we present a new complexity result for the gradient descent method with an appropriately fixed stepsize for minimizing a strongly convex function with locally -H…