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This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
We propose a MINRES-based Newton-type algorithm for solving unconstrained nonconvex optimization problems. Our approach uses the minimal residual method (MINRES), a well-known solver for indefinite symmetric linear systems, to compute…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
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…
Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…
This paper presents a canonical dual approach to the problem of minimizing the sum of a quadratic function and the ratio of nonconvex function and quadratic functions, which is a type of non-convex optimization problem subject to an…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…
We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular…
The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…
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…
Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…