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The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…
In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus…
A weighted sums of squares decomposition of positive Borel measurable functions on a bounded Borel subset of the Euclidean space is obtained via duality from the spectral theorem for tuples of commuting self-adjoint operators. The analogous…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…
This work presents several new results concerning the analysis of the convergence of binary, univariate, and linear subdivision schemes, all related to the {\it contractivity factor} of a convergent scheme. First, we prove that a convergent…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
Given a nonempty set $\mathcal{L}$ of linear orders, we say that the linear order $L$ is $\mathcal{L}$-convex embeddable into the linear order $L'$ if it is possible to partition $L$ into convex sets indexed by some element of $\mathcal{L}$…
This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…