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Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
In this paper, we tackle the problem of planning an optimal coverage path for a robot operating indoors. Many existing approaches attempt to discourage turns in the path by covering the environment along the least number of coverage lines,…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In order to solve the targeted {\bf QP} problems to a desired…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
In this paper we present some new, practical, geometric optimization techniques for computing polygon partitions, 1D and 2D point, interval, square and rectangle covers, as well as 1D and 2D interval and rectangle K-centers. All the…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this paper investigates the composite geodesically convex…
Although equirectangular projection (ERP) is a convenient form to store omnidirectional images (also known as 360-degree images), it is neither equal-area nor conformal, thus not friendly to subsequent visual communication. In the context…
This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…