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In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…
Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
We consider the problem of minimizing a block separable convex function (possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem…
Optimal transportation with capacity constraints, a variant of the well-known optimal transportation problem, is concerned with transporting one probability density $f \in L^1(\mathbb{R}^m)$ onto another one $g \in L^1(\mathbb{R}^n)$ so as…
We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary…
We study the minimization of convex, variational integrals of linear growth among all functions in the Sobolev space $W^{1,1}$ with prescribed boundary values (or its equivalent formulation as a boundary value problem for a degenerately…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
We study the Monge--Kantorovich problem with one-dimensional marginals $\mu$ and $\nu$ and the cost function $c = \min\{l_1, \ldots, l_n\}$ that equals the minimum of a finite number $n$ of affine functions $l_i$ satisfying certain…
Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing…
In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative…
In this paper, we study the global convergence of majorization minimization (MM) algorithms for solving nonconvex regularized optimization problems. MM algorithms have received great attention in machine learning. However, when applied to…
We develop a synthetic, variational framework for deriving comparison principles in infinite-dimensional Banach spaces. Unlike traditional approaches that rely on the regularity of minimizers and Euler--Lagrange equations, our method…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
Many modern distributed real-time signal sensing/monitoring systems require quantization for efficient signal representation. These distributed sensors often have inherent computational and energy limitations. Motivated by this concern, we…
Maximization and minimization problems of the principle eigenvalue for divergence form second order elliptic operators with the Dirichlet boundary condition are considered. The principal eigen map of such elliptic operators is introduced…
In this paper we analyze a mass transportation problem in a bounded domain with the possibility to transport mass to/from the boundary, paying the transport cost, that is given by the Euclidean distance plus an extra cost depending on the…