Related papers: Matrix Cubes Parametrized by Eigenvalues
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
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…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…
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…
This paper provides results for eigencurves associated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a, b, m) of continuous symmetric…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions.…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…