Related papers: Semidefinite representations of non-compact convex…
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 develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we…
In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
We study the maximization of sums of heterogeneous quadratic forms over the Stiefel manifold, a nonconvex problem that arises in several modern signal processing and machine learning applications such as heteroscedastic probabilistic…
In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…
For any truncated path algebra $\Lambda$ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties $\mathbf{Rep}_{\mathbf{d}}(\Lambda)$ of the $\Lambda$-modules with…
This paper considers polynomial optimization with unbounded sets. We give a homogenization formulation and propose a hierarchy of Moment-SOS relaxations to solve it. Under the assumptions that the feasible set is closed at infinity and the…
This paper investigates the minimization of the expectation of piecewise polynomial loss functions over Wasserstein balls. This optimization problem often appears as a key sub-problem of distributionally robust optimization problems. We…
In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…
In this paper, we propose a new convergent conic programming hierarchy of relaxations involving both semi-definite cone and second-order cone constraints for solving nonconvex polynomial optimization problems to global optimality. The…
Solution sets of systems of homogeneous linear equations over fields are characterized as being subspaces, i.e., sets that are closed under linear combinations. Our goal is to characterize solution sets of systems of equations over…
We consider the semi-infinite system of polynomial inequalities of the form \[ \mathbf{K}:=\{x\in\mathbb{R}^m\mid p(x,y)\ge 0,\ \ \forall y\in S\subseteq\mathbb{R}^n\}, \] where $p(x,y)$ is a real polynomial in the variables $x$ and the…
We provide an exhaustive analysis of the complete set of solutions of the equations of stellar equilibrium under semiclassical effects. As classical matter we use a perfect fluid of constant density; as the semiclassical source we use the…
Motivated by set estimation problems, we consider three closely related shape conditions for compact sets: positive reach, r-convexity and rolling condition. First, the relations between these shape conditions are analyzed. Second, we…
We formulate a class of nonlinear {evolution} partial differential equations (PDEs) as linear optimization problems on moments of positive measures supported on infinite-dimensional vector spaces. Using sums of squares (SOS) representations…
This article is concerned with the problem of approximating a not necessarily bounded spectrahedral shadow, a certain convex set, by polyhedra. By identifying the set with its homogenization the problem is reduced to the approximation of a…
The purpose of this paper is to provide tools for analyzing the compactness of sequences in Sobolev spaces, in particular if the sequence gets mapped onto a compact set by some nonlinear operator. Here, our focus lies on a very general…
Examples of exact categories in representation theory are given by the category of Delta-filtered modules over quasi-hereditary algebras, but also by various categories related to matrix problems, such as poset representations or…