Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform based schemes result in eecient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an ima...

subject to c(x) ≥ 0, where f : R → R and c : R → R are twice continuously differentiable functions. Let g(x) denote the gradient of f(x), and J(x) the mxn Jacobian matrix of c(x), with rows the gradients of c(x). A point x∗ is feasible with respect to the constraints c(x) if c(x∗) ≥ 0, and infeasible if c(x∗) < 0. The constraint ci(x) is considered active at x if ci(x) = 0 and inactive if ci(x)...

The numerical behavior of two implicit time-marching methods is investigated in solving two-dimensional unsteady compressible flows. The two methods are the second-order multistep backward differencing formula and the fourth-order multistage explicit first stage, single-diagonal coefficient, diagonally implicit Runge-Kutta scheme. A Newton-Krylov method is used to solve the nonlinear problem ar...

In [19], a general, inexact, e cient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the objective function is strongly convex. We also investigate a practical variant of t...

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the objective function is strongly convex. We also investigate a practical variant of...

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

We propose a general theory of parametric two-sided tropical linear systems based on the connections with zero-sum deterministic mean-payoff games. It is shown how this general theory specializes to particular tropical linear systems with parameter, arising from 1) the two-sided tropical eigenproblem Ax = λ+Bx and 2) the tropical linear programming. This involves 1) the problem of finding the s...

X iv :m at h/ 00 04 18 7v 1 [ m at h. H O ] 1 A pr 2 00 0 Journal of Nonlinear Mathematical Physics 2000, V.7, N 2, 244–262. (Re)-Examining the Past q-Newton Binomial: From Euler To Gauss Boris A. KUPERSHMIDT The University of Tennessee Space Institute, Tullahoma, TN 37388, USA E-mail: [email protected] Received March 6, 2000; Accepted April 7, 2000 Abstract A counter-intuitive result of Gauss ...

Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods‎, ‎we introduce two new parameters based on the modified secant equation proposed by Li et al‎. ‎(Comput‎. ‎Optim‎. ‎Appl‎. ‎202:523-539‎, ‎2007) with two approaches‎, ‎which use an extended new conjugacy condition‎. ‎The first is based on a modified descent three-term search direction‎, ‎as the descent Hest...

A technique for maintaining the positive definiteness of the matrices in the quasi-Newton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent to the constraint manifold is ensured by a so-called piecewise line-search technique, while their positive...