13 papers
Provable Parameter-Free Fixed-Point Algorithms with Linear Convergence Rates
Quoc Tran-Dinh, Pham Ngoc Anh, Ha Manh Tien
In this paper, we develop provable parameter-free and adaptive fixed-point algorithms for contractive mappings, with an emphasis on automatically exploiting hidden contractivity wi…
Adaptive Regularization within Trust Region Methods for Stochastic Nonconvex Optimization
Yunsoo Ha, Sara Shashaani, Quoc Tran-dinh
We propose a stochastic nonconvex optimization algorithm that achieves almost sure iteration complexity for problems with smooth objective function…
From Halpern's Fixed-Point Iterations to Nesterov's Accelerated Interpretations for Root-Finding Problems
Quoc Tran-Dinh
We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's…
Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions
Quoc Tran-Dinh, Nghia Nguyen-Trung
This paper develops new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method to solve a class of possibly nonmonotone stochastic composite inclu…
Lagrange Multipliers and Duality with Applications to Constrained Support Vector Machine
Nguyen Mau Nam, Gary Sandine, Quoc Tran-Dinh
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimizat…
A Class of Accelerated Fixed-Point-Based Methods with Delayed Inexact Oracles and Its Applications
Nghia Nguyen-Trung, Quoc Tran-Dinh
In this paper, we develop a novel accelerated fixed-point-based framework using delayed inexact oracles to approximate a fixed point of a nonexpansive operator (or equivalently, a…