Related papers: A Note on the Paper "Optimality Conditions for Vec…
Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $\phi:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of…
Suppose that X is a complex projective variety and L is a pseudo-effective divisor. A numerical reduction map is a quotient of X by all subvarieties along which L is numerically trivial. We construct two variants: the L-trivial reduction…
We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…
Many tasks in image processing can be tackled by modeling an appropriate data fidelity term $\Phi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}$ and then solve one of the regularized minimization problems \begin{align*}…
We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
The translation is not verbatim, many parts have been abbreviated and in some case alternative proofs were devised emphasizing intuition.
In [5] I solved the Thom's conjecture that a proper Thom map is triangulable. In this paper I drop the properness condition in the semialgebraic case and, moreover, in the definable case in an o-minimal structure.
In this short note the authors give answers to the three open problems formulated by Wu and Srivastava [{\it Appl. Math. Lett. 25 (2012), 1347--1353}]. We disprove the Problem 1, by showing that there exists a triangle which does not…
We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and…
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
A counter-example by Xiangchun Xiao, Guoping Zhao and Guorong Zhou in [J. Pseudo-Differ. Oper. Appl., (2021) 12:60] is incorrect. Further, there is no new characterization of weaving for g-frames by Xiangchun Xiao et al. in [2]. Xiangchun…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
In this paper we study continuous semigroups of positive operators on general vector lattices equipped with the relative uniform topology $\tau_{ru}$. We introduce the notions of strong continuity with respect to $\tau_{ru}$ and relative…
Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective…
For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov…