Related papers: On Matrices over a Polynomial Ring with Restricted…

The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see…

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…

The main aim of this work is to apply the matrix approach of ortho\-gonal polynomials associated with infinite Hermitian definite positive matrices in relation with an important question regarding the location of zeros of Sobolev orthogonal…

Let $O$ be a discrete valuation ring and $A := O[X_{m \times n}]/I_{m}(X)$ the determinantal ring of maximal minors. We consider algebra maps $\lambda \colon A \to O$, which is tantamount to choosing rank-deficient matrices $a \in O^{m…

We first show that a continuous function f is nonnegative on a closed set $K\subseteq R^n$ if and only if (countably many) moment matrices of some signed measure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite (if $K$…

We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of for00504925mulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in…

Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module. In this paper, we study and investigate some properties of $S$-primary submodules of $M$. Among the other results, it is…

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

Let $k$ be a field with characteristic zero, $R$ be the ring $k[x_1, \cdots, x_n]$ and $I$ be a monomial ideal of $R$. We study the Artinian local algebra $R/I$ when considered as an $R$-module $M$. We show that the largest reduced…

One of the central open problems to classify the computational complexity of finite-domain constraint satisfaction problems within P is to prove better algorithmic results for CSPs with a Maltsev polymorphism; we do not even know whether…

Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…

DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…

The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…

We show that a matrix is a Hermitian positive semidefinite matrix whose nonzero entries have modulus 1 if and only if it similar to a direct sum of all $1's$ matrices and a 0 matrix via a unitary monomial similarity. In particular, the only…

In connection with machine arithmetic, we are interested in systems of constraints of the form x + k \leq y + k'. Over integers, the satisfiability problem for such systems is polynomial time. The problem becomes NP complete if we restrict…

We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…

Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic…

Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…

We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…

Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…