17 citations · 39 across the 10 of their papers we have counts for
11 papers
Novel Optimization Techniques for Parameter Estimation
Chenyu Wu, Nuozhou Wang, Casey Garner +2
In this paper, we introduce a new optimization algorithm that is well suited for solving parameter estimation problems. We call our new method cubic regularized Newton with affine…
An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problems
Lei Zhao, Daoli Zhu, Shuzhong Zhang
In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like p…
Beyond Monotone Variational Inequalities: Solution Methods and Iteration Complexities
Kevin Huang, Shuzhong Zhang
In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify ex…
Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness
Casey Garner, Gilad Lerman, Shuzhong Zhang
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then…
A Gradient Complexity Analysis for Minimizing the Sum of Strongly Convex Functions with Varying Condition Numbers
Nuozhou Wang, Shuzhong Zhang
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (…
Cubic Regularized Newton Method for Saddle Point Models: a Global and Local Convergence Analysis
Kevin Huang, Junyu Zhang, Shuzhong Zhang
In this paper, we propose a cubic regularized Newton (CRN) method for solving convex-concave saddle point problems (SPP). At each iteration, a cubic regularized saddle point subpro…