Related papers: A strong convergence theorem for solving an equili…

We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…

In this paper we prove the strong and time-averaged strong convergence to equilibrium for solutions (with general initial data) of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. The assumption on the collision…

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for…

We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplified, 1…

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…

In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…

Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…

The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…

From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…

We study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with…

This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…