Related papers: Convexifying Multilinear Sets with Cardinality Con…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
Recently, finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing, image processing, statistical learning, and data sparse approximation. In this paper, we…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
Motivated by previous efforts toward mathematically analyzing the treatment of monomials in spatial branch-and-bound, we study the convex hull of the graph of a simple monomial on a nonnegative box domain in arbitrary dimension, where at…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a…
We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…
We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…
In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…
We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…
Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying…
In this article a class of closed convex sets in the Euclidean $n$-space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\cite{Lay:1982} to a class of closed non-compact convex sets is…
In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…