相关论文: DC algorithms for a class of sparse group $\ell_0$…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that…
An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…
The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
In this paper, we develop a new computational approach which is based on minimizing the difference of two convex functionals (DC) to solve a broader class of phase retrieval problems. The approach splits a standard nonlinear least squares…
We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function.…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…
This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…
We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…
We study the classical coalition structure generation (CSG) problem and compare the anytime behavior of three algorithmic paradigms: dynamic programming (DP), MILP branch-and-bound, and sparse relaxations based on greedy or $l_1$-type…
We present a continuous nonlinear optimization model for the Spin Glass Problem (SGP), building on a classical result by Rosenberg (1972), which shows that for a class of multilinear polynomial problems the optimal values of the continuous…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…