Related papers: De-singularity Subgradient for the $q$-th-Powered …
The extended Weber location problem is a classical optimization problem that has inspired some new works in several machine learning scenarios recently. However, most existing algorithms may get stuck due to the singularity at the data…
The $\ell_p$ regularization problem with $0< p< 1$ has been widely studied for finding sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. The proximal gradient…
This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different $\ell_p$ norms in the demand points. We analyze the difficulty of this family of problems and revisit…
We propose an algorithm for the Wireless Sensor Network localization problem, which is based on the well-known algorithmic framework of Alternating Minimization. We start with a non-smooth and non-convex minimization, and transform it into…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
The Weber problem consists of finding a point in $\mathbbm{R}^n$ that minimizes the weighted sum of distances from $m$ points in $\mathbbm{R}^n$ that are not collinear. An application that motivated this problem is the optimal location of…
We consider gradient descent like algorithms for Support Vector Machine (SVM) training when the data is in relational form. The gradient of the SVM objective can not be efficiently computed by known techniques as it suffers from the…
We study the solvability of the regularity problem for degenerate elliptic operators in the block case for data in weighted spaces. More precisely, let $L_w$ be a degenerate elliptic operator with degeneracy given by a fixed weight $w\in…
We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…
This paper introduces a subgradient extragradient algorithm with a conjugate gradient-type direction to solve pseudomonotone variational inequality problems in Hilbert spaces. The algorithm features a self-adaptive strategy that eliminates…
We theoretically study the fundamental problem of learning a single neuron with a bias term ($\mathbf{x} \mapsto \sigma(<\mathbf{w},\mathbf{x}> + b)$) in the realizable setting with the ReLU activation, using gradient descent. Perhaps…
This paper investigates numerical solution methods for the Schatten-$p$ quasi-norm regularized problem with $p \in [0,1]$, which has been widely studied for finding low-rank solutions of linear inverse problems and gained successful…
We present an iterative support shrinking algorithm for $\ell_{p}$-$\ell_{q}$ minimization~($0 <p < 1 \leq q < \infty $). This algorithm guarantees the nonexpensiveness of the signal support set and can be easily implemented after being…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…
In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global…
We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…