Related papers: Optimization hierarchies for distance-avoiding set…

Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster…

This research studies a non-convex geometric optimization problem arising from the field of optical wireless power transfer. In the considered optimization problem, the cost function is a sum of negatively and fractionally powered distances…

Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…

Given an open set $T\subset [-1,1)$, we introduce the concepts of $T$-avoiding spherical codes and designs, that is, spherical codes that have no inner products in the set $T$. We show that certain codes found in the minimal vectors of the…

This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of distances between points to the context of three-point…

In this paper convex optimization techniques are employed for convex optimization problems in infinite dimensional Hilbert spaces. A first order optimality condition is given. Let $f : \mathbb{R}^{n}\rightarrow \mathbb{R}$ and let $x\in…

In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that…

A longstanding open problem in coding theory is to determine the best (asymptotic) rate $R_2(\delta)$ of binary codes with minimum constant (relative) distance $\delta$. An existential lower bound was given by Gilbert and Varshamov in the…

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…

Semidefinite Optimization has become a standard technique in the landscape of Mathematical Programming that has many applications in finite dimensional Quantum Information Theory. This paper presents a way for finite-dimensional relaxations…

Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian…

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)…

In this paper, we consider set optimization problems where the solution concept is given by the set approach. Specifically, we deal with the lower less and the upper less set relations. First, we derive the convexity and Lipschitzianity of…

Quantum contextuality is usually revealed by the non-contextual inequality, which can always be associated with an exclusivity graph. The quantum upper bound of the inequality is nothing but the Lov\'asz number of the graph. In this work,…

This paper is dedicated to the spectral optimization problem $$ \mathrm{min}\left\{\lambda_1^s(\Omega)+\cdots+\lambda_m^s(\Omega) + \Lambda \mathcal{L}_n(\Omega)\colon \Omega\subset D \mbox{ s-quasi-open}\right\} $$ where $\Lambda>0,…

This paper deals with Riemannian optimization on the unit sphere in terms of $p$-norm with general $p > 1$. As a Riemannian submanifold of the Euclidean space, the geometry of the sphere with $p$-norm is investigated, and several geometric…

In this paper, we prove that the global version of the ${\L}$ojasiewicz gradient inequality holds for quadratic sphere constrained optimization problem with exponent $\theta=\frac{3}{4}$. An example from Ting Kei Pong shows that…

This paper considers sparse polynomial optimization with unbounded sets. When the problem possesses correlative sparsity, we propose a sparse homogenized Moment-SOS hierarchy with perturbations to solve it. The new hierarchy introduces one…

For a given graph $G$, a "hopset" $H$ with hopbound $\beta$ and stretch $\alpha$ is a set of edges such that between every pair of vertices $u$ and $v$, there is a path with at most $\beta$ hops in $G \cup H$ that approximates the distance…

In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…