Search Results - "LEWIS, ADRIAN S."

Nonsmooth optimization via quasi-Newton methods by Lewis, Adrian S., Overton, Michael L.

“…We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f , not necessarily convex. We introduce an inexact line search…”
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Alternating Projections on Manifolds by Lewis, Adrian S, Malick, Jerome

“…We prove that if two smooth manifolds intersect transversally, then the method of alternating projections converges locally at a linear rate. We bound the…”
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Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods by Drusvyatskiy, Dmitriy, Lewis, Adrian S.

“…The proximal gradient algorithm for minimizing the sum of a smooth and nonsmooth convex function often converges linearly even without strong convexity. One…”
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Stabilization via Nonsmooth, Nonconvex Optimization by Burke, J.V., Henrion, D., Lewis, A.S., Overton, M.L.

“…Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex…”
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Generic nondegeneracy in convex optimization by DRUSVYATSKIY, DMITRIY, LEWIS, ADRIAN S.

“…lower- \mathbf{C}^2 functions…”
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Variational analysis of the Crouzeix ratio by Greenbaum, Anne, Lewis, Adrian S., Overton, Michael L.

“…Let W ( A ) denote the field of values (numerical range) of a matrix A . For any polynomial p and matrix A , define the Crouzeix ratio to have numerator max |…”
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Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions by Drusvyatskiy, Dmitriy, Ioffe, Alexander D., Lewis, Adrian S.

“…Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally…”
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Generic Optimality Conditions for Semialgebraic Convex Programs by Bolte, Jérôme, Daniilidis, Aris, Lewis, Adrian S.

“…We consider linear optimization over a nonempty convex semialgebraic feasible region F . Semidefinite programming is an example. If F is compact, then for…”
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Differentiability of cone-monotone functions on separable Banach space by BORWEIN, Jonathan M, BURKE, James V, LEWIS, Adrian S

“…Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued…”
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Level set methods for finding critical points of mountain pass type by Lewis, Adrian S., Pang, C.H. Jeffrey

“…Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the…”
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Dykstras algorithm with bregman projections: A convergence proof by Bauschke, Heinz H, Lewis, Adrian S

“…Dykstra's algorithm and the method of cyclic Bregman projections are often employed to solve best approximation and convex feasibility problems, which are…”
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Variational analysis of functions of the roots of polynomials by BURKE, James V, LEWIS, Adrian S, OVERTON, Michael L

“…The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential of the abscissa mapping…”
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Randomized Methods for Linear Constraints: Convergence Rates and Conditioning by Leventhal, D., Lewis, A. S.

“…We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear…”
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Variational Analysis of the Abscissa Mapping for Polynomials via the Gauss-Lucas Theorem by Burke, James V, Lewis, Adrian S, Overton, Michael L

“…Consider the linear space [Weierstrass p]n of polynomials of degree n or less over the complex field. The abscissa mapping on [Weierstrass p]n is the mapping…”
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Quadratic expansions of spectral functions by Lewis, Adrian S., Sendov, Hristo S.

“…A function, F, on the space of n×n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument, that is F(A)=F(UAUT) for…”
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Self-concordant barriers for hyperbolic means by LEWIS, Adrian S, SENDOV, Hristo S

“…The geometric mean and the function (det(·))^sup 1/m^ (on the m-by-m positive definite matrices) are examples of "hyperbolic means": functions of the form…”
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Lipschitz minimization and the Goldstein modulus by Kong, Siyu, Lewis, Adrian S

“…Goldstein's 1977 idealized iteration for minimizing a Lipschitz objective fixes a distance - the step size - and relies on a certain approximate subgradient…”
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The complexity of first-order optimization methods from a metric perspective by Lewis, Adrian S, Tian, Tonghua

“…A central tool for understanding first-order optimization algorithms is the Kurdyka-Lojasiewicz inequality. Standard approaches to such methods rely crucially…”
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Local geometry of feasible regions via smooth paths by Lewis, Adrian S, Nicolae, Adriana, Tian, Tonghua

“…Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds…”
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Recognizing weighted means in geodesic spaces by Goodwin, Ariel, Lewis, Adrian S, Lopez-Acedo, Genaro, Nicolae, Adriana

“…Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse…”
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