Related papers: Semi-definite programming and functional inequalit…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We examine the problem of approximating a positive, semidefinite matrix $\Sigma$ by a dyad $xx^T$, with a penalty on the cardinality of the vector $x$. This problem arises in sparse principal component analysis, where a decomposition of…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
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…
In this work we study the polytope associated with a 0,1-integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
We initiate the study of parallel quantum programming by defining the operational and denotational semantics of parallel quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
For a family of infinite-dimensional diffusions with degenerate noise, we develop a modified $\Gamma$ calculus on finite-dimensional projections of the equation in order to produce explicit functional inequalities that can be scaled to…
In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…
It is shown by a counterexample that isocapacitary and isoperimetric constants of a multi-dimensional Euclidean domain starshaped with respect to a ball are not equivalent. Sharp integral inequalities involving the harmonic capacity which…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
In this paper, we study parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function. We study the behavior of the optimal partition and optimal set mapping on a so-called nonlinearity…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…