Related papers: Block Coordinate Descent Methods for Optimization …
In this letter, we first propose a \underline{Z}eroth-\underline{O}rder c\underline{O}ordinate \underline{M}ethod~(ZOOM) to solve the stochastic optimization problem over a decentralized network with only zeroth-order~(ZO) oracle feedback…
This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…
The so-called Burer-Monteiro method is a well-studied technique for solving large-scale semidefinite programs (SDPs) via low-rank factorization. The main idea is to solve rank-restricted, albeit non-convex, surrogates instead of the SDP.…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical…
Dynamic polarization control (DPC) is beneficial for many optical applications. It uses adjustable waveplates to perform automatic polarization tracking and manipulation. Efficient algorithms are essential to realizing an endless…
Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such…
We study stochastic decentralized optimization for the problem of training machine learning models with large-scale distributed data. We extend the widely used EXTRA and DIGing methods with variance reduction (VR), and propose two methods:…
Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
A general method to describe stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems. The determination of an optimal coordinate for the description of stochastic dynamics. The reconstruction of…
This paper introduces the Fej\'er-monotone hybrid steepest descent method (FM-HSDM), a new member to the HSDM family of algorithms, for solving affinely constrained minimization tasks in real Hilbert spaces, where convex smooth and…
Kernel methods are powerful tools for nonlinear learning with well-established theory. The scalability issue has been their long-standing challenge. Despite the existing success, there are two limitations in large-scale kernel methods: (i)…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
The joint bidiagonalization(JBD) process is a useful algorithm for the computation of the generalized singular value decomposition(GSVD) of a matrix pair. However, it always suffers from rounding errors, which causes the Lanczos vectors to…
Decentralized nonconvex optimization has received increasing attention in recent years in machine learning due to its advantages in system robustness, data privacy, and implementation simplicity. However, three fundamental challenges in…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…