相关论文: Decreasing Minimization on M-convex Sets: Backgrou…

The concept of a monitoring edge-geodetic set (MEG-set) in a graph $G$, denoted $MEG(G)$, refers to a subset of vertices $MEG(G)\subseteq V(G)$ such that every edge $e$ in $G$ is monitored by some pair of vertices $ u, v \in MEG(G)$, where…

We develop a deterministic zeroth-order mirror descent framework by replacing gradients with a general vector field, yielding a vector-field-driven mirror update that preserves Bregman geometry while accommodating derivative-free oracles.…

In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…

In this paper we present a complete characterization of the smallest sets which block all the simple perfect matchings in a complete convex geometric graph on $2m$ vertices. In particular, we show that all these sets are caterpillar graphs…

We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two…

We characterize relative notions of syndetic and thick sets using, what we call, "derived" sets along ultrafilters. Manipulations of derived sets is a characteristic feature of algebra in the Stone-\v{C}ech compactification and its…

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic…

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…

We explore the concept of separating systems of vertex sets of graphs. A separating system of a set $X$ is a collection of subsets of $X$ such that for any pair of distinct elements in $X$, there exists a set in the separating system that…

All matrices we consider have entries in a fixed algebraically closed field $K$. A minor of a square matrix is principal means it is defined by the same row and column indices. We study the ideal generated by size $t$ principal minors of a…

(Block-)coordinate minimization is an iterative optimization method which in every iteration finds a global minimum of the objective over a variable or a subset of variables, while keeping the remaining variables constant. While for some…

A minimal separating set in a connected topological space $X$ is a subset $L \subset X$ with the property that $X \setminus L$ is disconnected, but if $L^{\prime}$ is a proper subset of $L$, then $X \setminus L^{\prime}$ is connected. Such…

We consider the rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…

The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…

Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A…

This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…

We consider numbers and sizes of independent sets in graphs with minimum degree at least $d$, when the number $n$ of vertices is large. In particular we investigate which of these graphs yield the maximum numbers of independent sets of…

Let $P$ be a set of $n$ points in general position on the plane. A set of closed convex polygons with vertices in $P$, and with pairwise disjoint interiors is called a convex decomposition of $P$ if their union is the convex hull of $P$,…