Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graph...

Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that ...

Adversarial attacks on controllers of dynamic systems have become a serious threat to many real-world systems, making methods for fast identification an indispensable part autonomous systems. With the increasing use model-based controllers, it is valid exploit model knowledge also attack as long privacy individual components maintained. A scalable, method reveal generic was introduced in our pr...

Minimizing a convex function of measure with sparsity-inducing penalty is typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this can be solved by discretizing the and running non-convex gradient descent on positions weights particles. For measures d-dimensional manifold under some non-degeneracy assumptions, leads to global optimiz...

In recent years there has been growing interest in convex optimization techniques for system identification and time series modeling. This interest is motivated by the success of convex methods for sparse optimization and rank minimization in signal processing, statistics, and machine learning, and by the development of new classes of algorithms for large-scale nondifferentiable convex optimiza...

Tensor methods for unconstrained optimization were rst introduced by Schn-abel and Chow SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate-size problems. The major contribution of this paper is the extension of these methods to large, sparse unconstrained optimization problems. This extension requires an entirely new way of solving the tensor model th...

This paper proposes solution to the following non-convex optimization problem: min || x || p subject to || y Ax || q Such an optimization problem arises in a rapidly advancing branch of signal processing called ‘Compressed Sensing’ (CS). The problem of CS is to reconstruct a k-sparse vector xnX1, from noisy measurements y = Ax+ , where AmXn (m<n) is the measurement matrix and mX1 is additive no...