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We consider the problem of minimizing a convex function over a subset of R^n that is not necessarily convex (minimization of a convex function over the integer points in a polytope is a special case). We define a family of duals for this…

Effective and reliable screening of patients via Computer-Aided Diagnosis can play a crucial part in the battle against COVID-19. Most of the existing works focus on developing sophisticated methods yielding high detection performance, yet…

In [1] the problem of finding a sharp lower bound on lower against number of a general graph is mentioned as an open question. We solve the problem by establishing a tight lower bound on lower against number of a general graph in terms of…

The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…

We prove an abstract criterion that a surjective convolution operator in spaces of analytic functions on convex subsets of the complex plane has a continuous linear right inverse. Considered convex sets have a countable neighborhood basis…

Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…

We consider the problem of managing a dynamic heterogeneous storage system in a distributed way so that the amount of data assigned to a host in that system is related to its capacity. Two central problems have to be solved for this: (1)…

In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…

This paper discusses differential stability of convex programming problems in Hausdorff locally convex topological vector spaces. Among other things, we obtain formulas for computing or estimating the subdifferential and the singular…

Inverse problem relatively domain for the plate under across vibrations is considered. The definition of s-functions is interoduced. The construction for defining of the domain of the plate by given s-functions is offered.

This paper outlines our submission for the 4th COV19D competition as part of the `Domain adaptation, Explainability, Fairness in AI for Medical Image Analysis' (DEF-AI-MIA) workshop at the Computer Vision and Pattern Recognition Conference…

This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

We show that the copolarity of pseudo-cones has analogous properties as the usual polarity of convex bodies.

A recent result on the Gauss image problem for pseudo-cones can be interpreted as a measure transport, performed by the reverse radial Gauss map of a pseudo-cone. We find a cost function that is minimized by this transport map, and we prove…

We present some complexity results concerning the problems of covering a graph with $p$ convex sets and of partitioning a graph into $p$ convex sets. The following convexities are considered: digital convexity, monophonic convexity,…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

In this paper we consider convex subsets of locally-convex topological vector spaces. Given a fixed point in such a convex subset, we show that there exists a curve completely contained in the convex subset and leaving the point in a given…

In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…

We establish upper bounds for the expected excess risk of models trained by proper iterative algorithms which approximate the local minima. Unlike the results built upon the strong globally strongly convexity or global growth conditions…