Related papers: Polynomial Matrix Inequalities within Tame Geometr…

We study the problem of learning a tensor from a set of linear measurements. A prominent methodology for this problem is based on a generalization of trace norm regularization, which has been used extensively for learning low rank matrices,…

This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…

Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…

This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…

We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization

A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be…

We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…

In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In…

We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…

We use the concept of barrier-based smoothing approximations introduced in [ C. B. Chua and Z. Li, A barrier-based smoothing proximal point algorithm for NCPs over closed convex cones, SIOPT 23(2), 2010] to extend the non-interior…

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…

We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, "tame"). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the…

Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a…

In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…

This paper studies the saddle point problem of polynomials. We give an algorithm for computing saddle points. It is based on solving Lasserre's hierarchy of semidefinite relaxations. Under some genericity assumptions on defining…

Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $\ell_0$ norm. In this paper, a special type of tensor complementarity problems with…

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…