Related papers: On the minimal distance between two surfaces

Although the Karush-Kuhn-Tucker conditions suggest a connection between a conic optimization problem and a complementarity problem, it is difficult to find an accessible explicit form of this relationship in the literature. This note will…

In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…

There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…

We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…

We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…

In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…

We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for…

We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…

We consider dual optimization problems to the fundamental problem of finding the minimum distance from a point to a subspace. We provide a counterexample to a theorem which has appeared in the literature, relating the minimum distance…

In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional…

The idea of minimum distance, familiar from R <-> 1/R duality when the string target space is a circle, is analyzed for less trivial geometries. The particular geometry studied is that of a blown-up quotient singularity within a Calabi-Yau…

The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…

Distributed optimization has gained substantial interest in recent years due to its wide applications in machine learning. However, most of existing algorithms are designed for Euclidean spaces, leaving composite optimization on Riemannian…

We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $\epsilon$-regularity result for optimal transport maps…

We consider the extragradient method to minimize the sum of two functions, the first one being smooth and the second being convex. Under the Kurdyka-Lojasiewicz assumption, we prove that the sequence produced by the extragradient method…

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

An interesting problem in classical differential geometry is to find methods to prove that two surfaces defined by different charts actually coincide up to position in space. In a previous paper we proposed a method in this direction for…

Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances…

We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…