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This paper is devoted to the generalized differential study of the normal cone mappings associated with a large class of parametric constraint systems (PCS) that appear, in particular, in nonpolyhedral conic programming. Conducting a local…
In this article, we introduce a novel concept for second-order information of a nonsmooth function inspired by the Goldstein eps-subdifferential. It comprises the coefficients of all existing second-order Taylor expansions in an eps-ball…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This…
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for strongly-convex and smooth functions. Our analysis is much simpler in contrast to a similar…
We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that…
We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…
Person search aims to localize specific a target person from a gallery set of images with various scenes. As the scene of moving pedestrian changes, the captured person image inevitably bring in lots of background noise and foreground noise…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
A novel algorithm for wide-baseline matching called MODS - Matching On Demand with view Synthesis - is presented. The MODS algorithm is experimentally shown to solve a broader range of wide-baseline problems than the state of the art while…
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…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of…