Related papers: Critical Topology for Optimization on the Symplect…

A study of symplectic actions of a finite group $G$ on smooth 4-manifolds is initiated. The central new idea is the use of $G$-equivariant Seiberg-Witten-Taubes theory in studying the structure of the fixed-point set of these symmetries.…

Motivated by and extending the technical results in our earlier work on symplectic Calabi-Yau $4$-manifolds, a general and systematic approach for studying certain unions of symplectic embedded surfaces in a rational $4$-manifold $X=CP^2\#…

This paper studies sufficient conditions in a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of admissible curves, which depends on an artificial potential…

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

In this paper, we explore the bifurcation phenomena and establish the existence of multiple solutions for the nonlocal subelliptic Brezis-Nirenberg problem: \begin{equation*} \begin{cases} (-\Delta_{\mathbb{G}})^s u= |u|^{2_s^*-2}u+\lambda…

Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…

In this paper, we investigate the subelliptic nonlocal Brezis-Nirenberg problem on stratified Lie groups involving critical nonlinearities, namely, \begin{align*} (-\Delta_{\mathbb{G}, p})^s u&= \mu |u|^{p_s^*-2}u+\lambda h(x, u) \quad…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank-one terms. Use is made of the rich symmetry structure to construct infinite families of critical points…

The goal of this paper is to describe a method to solve a class of time optimal control problems which are equivalent to finding the sub-Riemannian minimizing geodesics on a manifold M. In particular, we assume that the manifold M is acted…

This article announces a series of articles aiming at introducing the concept of symplectic spinors into symplectic topology resp. the concept of Frobenius structures. We will give lower bounds for the number of fixed points of a…

In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…

Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing symmetries. Following recent works, which generalized the classical concept of static turnpike to manifold turnpike, we extend the exponential…

Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…

Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…

Periodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries…