相关论文: On the number of vertices in integer linear progra…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise…
An integer partition \lambda of n corresponds, via its Ferrers diagram, to an artinian monomial ideal I of colength n in the polynomial ring on two variables. If the partition \lambda corresponds to an integrally closed ideal we call…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
In this article we study convex integer maximization problems with composite objective functions of the form $f(Wx)$, where $f$ is a convex function on $\R^d$ and $W$ is a $d\times n$ matrix with small or binary entries, over finite sets…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to…
Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…
We give some sufficient conditions of separation of two sets of integer points by a hyperplane. Our conditions are related to the notion of convexity of sets of integer points and are weaker than existing notions.
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…
An integer vector $b \in \mathbb{Z}^d$ is a degree sequence if there exists a hypergraph with vertices $\{1,\dots,d\}$ such that each $b_i$ is the number of hyperedges containing $i$. The degree-sequence polytope $\mathscr{Z}^d$ is the…
We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…