Related papers: Chasing Positive Bodies
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
We consider the problem of recovering a low-rank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been shown that this problem can be solved…
Recent methods for learning a linear subspace from data corrupted by outliers are based on convex $\ell_1$ and nuclear norm optimization and require the dimension of the subspace and the number of outliers to be sufficiently small. In sharp…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
A greedy pursuit strategy which finds a common basis for approximating a set of similar signals is proposed. The strategy extends the Optimized Orthogonal Matching Pursuit approach to selecting the subspace containing the approximation of…
In recent years we have witnessed an increase on the development of methods for submodular optimization, which have been motivated by the wide applicability of submodular functions in real-world data-science problems. In this paper, we…
We consider an online matching problem with concave returns. This problem is a significant generalization of the Adwords allocation problem and has vast applications in online advertising. In this problem, a sequence of items arrive…
The main contribution of this paper resides in providing novel algorithmic advances and analytical insights for the sequential hiring problem, a recently introduced dynamic optimization model where a firm adaptively fills a limited number…
We take a systematic look at the problem of storing whole files in a cache with limited capacity in the context of optimistic learning, where the caching policy has access to a prediction oracle (provided by, e.g., a Neural Network). The…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
We present a fast trajectory optimization algorithm for the soft capture of uncooperative tumbling space objects. Our algorithm generates safe, dynamically feasible, and minimum-fuel trajectories for a six-degree-of-freedom servicing…
This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…
Recent progress in robotic manipulation has dealt with the case of previously unknown objects in the context of relatively simple tasks, such as bin-picking. Existing methods for more constrained problems, however, such as deliberate…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…
Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult.…
We consider the following problem in computational geometry: given, in the d-dimensional real space, a set of points marked as positive and a set of points marked as negative, such that the convex hull of the positive set does not intersect…
We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on the leader's decision. The resulting random variable is…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…