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We consider the resource allocation problem and its numerical solution. The following constructions are demonstrated: 1) Walrasian price-adjustment mechanism for determining the equilibrium; 2) Decentralized role of the prices; 3) Slater's…
We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In…
We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear…
A class of averaging block nonlinear Kaczmarz methods is developed for the solution of the nonlinear system of equations. The convergence theory of the proposed method is established under suitable assumptions and the upper bounds of the…
In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, being based on a splitting technique…
In this work, we propose a method combining the Sinc collocation method with the double exponential transformation for computing the eigenvalues of the anharmonic Coulombic potential. We introduce a scaling factor that improves the…
Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve…
We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same authors, where the authors presented a sinc-function based…
Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
A new algorithm for time dependent Hamilton Jacobi equations on networks, based on semi Lagrangian scheme, is proposed. It is based on the definition of viscosity solution for this kind of problems recently given in. A thorough convergence…
In this paper we demonstrate that the numerical method of steepest descent fails when applied in a straight forward fashion to the most commonly occurring highly oscillatory integrals in scattering theory. Through a polar change of…