Related papers: Grothendieck-type inequalities in combinatorial op…
We study a sharp fractional Moser-Trudinger type inequality in dimension 1, its compactness properties and the critical points of a functional associeted to the inequality.
Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper error bounds of such…
A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general…
In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology,…
Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…
The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we study conjugate…
We compute the Grothendieck group of the category of abelian varieties over an algebraically closed field $k$. We also compute the Grothendieck group of the category of $A$-isotypic abelian varieties, for any simple abelian variety $A$,…
This report formulates a conjectural combinatorial rule that positively expands Grothendieck polynomials into Lascoux polynomials. It generalizes one such formula expanding Schubert polynomials into key polynomials, and refines another one…
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
The application of combinatorial optimization problems to solving the problems of planning processes for industries based on a fund of reconfigurable production resources is considered. The results of their solution by mixed integer…
Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…
The probabilistic analysis of condition numbers has traditionally been approached from different angles; one is based on Smale's program in complexity theory and features integral geometry, while the other is motivated by geometric…
We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--Wachs inequality and generalize it to inequalities on order polynomials and their $q$-analogues via direct…
In this paper we prove several inequalities by means of diagrammatic expansions, a technique already used in [BG13]. This time we show that iterations of the folding of a probability leads to the proof of some in- equalities by means of a…
We describe some combinatorial problems in finite projective planes and indicate how R\'edei's theory of lacunary polynomials can be applied to them.
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…
We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker coefficients in the context of the Geometric Complexity Theory program to prove a variant of Valiant's algebraic analog of the P not equal to NP conjecture.…