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Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…
In this paper, we extend the previous convergence results for the generalized alternating projection method applied to subspaces in [arXiv:1703.10547] to hold also for smooth manifolds. We show that the algorithm locally behaves similarly…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
Black-box optimization is primarily important for many compute-intensive applications, including reinforcement learning (RL), robot control, etc. This paper presents a novel theoretical framework for black-box optimization, in which our…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
The selection of the most appropriate algorithm to solve a given problem instance, known as algorithm selection, is driven by the potential to capitalize on the complementary performance of different algorithms across sets of problem…
In this paper, we provide a sub-gradient based algorithm to solve general constrained convex optimization without taking projections onto the domain set. The well studied Frank-Wolfe type algorithms also avoid projections. However, they are…
Finding approximate stationary points, i.e., points where the gradient is approximately zero, of non-convex but smooth objective functions $f$ over unrestricted $d$-dimensional domains is one of the most fundamental problems in classical…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
In this paper, we study the standard formulation of an optimization problem when the computation of gradient is not available. Such a problem can be classified as a "black box" optimization problem, since the oracle returns only the value…
We introduce a novel distributed derivative-free optimization framework that is resilient to stragglers. The proposed method employs coded search directions at which the objective function is evaluated, and a decoding step to find the next…