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We prove existence and convergence of sequences generated by the proximal point method and its two variants for monotone vector fields in Hadamard spaces. Before obtaining our results, we investigate some fundamental properties of tangent…
In this paper, we proposed an alternating projection based algorithm to solve a class of distributed MIN-MAX convex optimization problems. We firstly transform this MINMAX problem into the problem of searching for the minimum distance…
Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance…
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a…
For covariance-based image descriptors, taking into account the curvature of the corresponding feature space has been shown to improve discrimination performance. This is often done through representing the descriptors as points on…
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…
We consider the problem of minimizing a function over the manifold of orthogonal matrices. The majority of algorithms for this problem compute a direction in the tangent space, and then use a retraction to move in that direction while…
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…
We extend coordinate descent to manifold domains, and provide convergence analyses for geodesically convex and non-convex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and…
In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
Visual data such as videos are often sampled from complex manifold. We propose leveraging the manifold structure to constrain the deep action feature learning, thereby minimizing the intra-class variations in the feature space and…
We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global…
Considering orthogonal Stiefel manifolds as constraint manifolds, we give an explicit description of a set of local coordinates that also generate a basis for the tangent space in any point of the orthogonal Stiefel manifolds. We show how…
A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
In this paper, we propose a distributed algorithm to solve planar minimum time multi-vehicle rendezvous problem with non-identical velocity constraints on cyclic digraph (topology). Motivated by the cyclic alternating projection method that…
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…