Related papers: The P\'olya-Tchebotarev problem with semiclassical…

I consider the Hermitean two-matrix model with a logarithmic potential which is associated in the one-matrix case with the Penner model. Using loop equations I find an explicit solution of the model at large N (or in the spherical…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

We show that the momentum, the density, and the electromagnetic field associated with the massive KleinGordon-Maxwell equations converge in the semi-classical limit towards their respective equivalents associated with the relativistic…

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means…

We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a…

The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated to pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the…

In power systems, large-scale optimisation problems are extensively used to plan for capacity expansion at the supra-national level. However, their cost-optimal solutions are often not exploitable by decision-makers who are preferably…

The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…

In this paper we develop a numerical method for solving a class of optimization problems known as optimal location or quantization problems. The target energy can be written either in terms of atomic measures and the Wasserstein distance or…

Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact…

Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…

We consider the problem of finding a best uniform approximation to the standard monomial on the unit ball in $\bbC^2$ by polynomials of lower degree with complex coefficients. We reduce the problem to a one-dimensional weighted minimization…

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…

We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…

Many theorems about Kolmogorov complexity rely on existence of combinatorial objects with specific properties. Usually the probabilistic method gives such objects with better parameters than explicit constructions do. But the probabilistic…

We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this…

Minimax single facility location problems in multidimensional space with Chebyshev distance are examined within the framework of idempotent algebra. The aim of the study is twofold: first, to give a new algebraic solution to the location…

We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic curves. Coppersmith's method uses lattice basis reduction to…

Since the work [13] by Guo [Invent. Math. 153 (2003), no. 3, 593--630], how to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov-Maxwell-Boltzmann system with the whole range of soft…