Related papers: Schatten-$p$ Quasi-Norm Regularized Matrix Optimiz…

On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many…

Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…

We investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…

We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation,…

We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes…

This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

Recently, Bai and Benzi proposed a class of regularized Hermitian and skew-Hermitian splitting methods (RHSS) iteration methods for solving the nonsingular saddle point problem. In this paper, we apply this method to solve the singular…

The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, Lanczos bidiagonalization based LSQR and its mathematically equivalent CGLS are most commonly used. They have intrinsic…

We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local…

Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…

The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…

Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…

Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…

Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However,…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…