Related papers: On the R$_0$-tensors and the solution map of tenso…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.
We consider the problem of determining the closure of a quadratic module M in a commutative R-algebra with respect to the finest locally convex topology. This is of interest in deciding when the moment problem is solvable and in analyzing…
A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such…
In this thesis, we present results related to complementarity problems. We study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
We study the properties of the free boundaries and the corresponding hitting times in the context of optimal stopping in discrete time. We first prove the continuity of the map from the boundaries to the expected value of the corresponding…
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…
Using techniques developed in [Lasserre02], we show that some minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinite…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…
Does a given a set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this…
The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
We introduce an extended tangent cone of high order to a set and study its properties. Then we use this local approximation for deriving high-order necessary conditions for local minimizers of constrained optimization problems.
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively. An order topology is introduced such that…
We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…