Related papers: Constraint Maps: Insights and Related Themes
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part and the projected image to the constraint, one can prove…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms…
We prove full boundary regularity for minimizing biharmonic maps with smooth Dirichlet boundary conditions. Our result, similarly as in the case of harmonic maps, is based on the nonexistence of nonconstant boundary tangent maps. With the…
Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. While some constraints are hard and as such must be satisfied with zero-tolerance,…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…
In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps. The note includes a brief historical perspective and…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
Many problems in high-dimensional statistics and optimization involve minimization over nonconvex constraints-for instance, a rank constraint for a matrix estimation problem-but little is known about the theoretical properties of such…
In a closed, oriented ambient manifold $(M^n,g)$ we consider the problem of finding $\mathbb{S}^1$-valued harmonic maps with prescribed singular set. We show that the boundary of any oriented $(n-1)$-submanifold can be realised as the…
Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…
We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem…
The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…