In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmann manifolds or a product of Grassmann manifolds. Specifically we defined bfgs and l-bfgs updates in local and global coordinates on Grassmann manifolds or a product of these. We proved that, when local coordinates are used, our bfgs updates on Grassmann manifolds share the s...

In this paper, we propose an approach to the multichannel blind deconvolution problem, based on the mutual information criterion and more generally on an appropriate system of estimating equations. Formulas for the quasiNewton algorithm and the asymptotic covariance matrix of the estimator are provided. More interesting results have been obtained in the pure deconvolution case. By a clever para...

In modeling and location analysis, most traditional fault location methods do not consider about the existence of practical nonlinear model in distribution network, such as the nonlinearity of load and grounding resistor. Hence, the adopted model can’t express the practical network, and the location results will lose practical meaning. Aiming at solving the question above, this paper proposes a...

The Radiotherapy treatment planning optimization process based on a quasi-Newton algorithm with an object function containing dose-volume constraints is not guaranteed to converge when the dose value in the dose-volume constraint is a critical value of the dose distribution. This is caused by finite differentiability of the dose-volume histogram at such values. A closer look near such values re...

In this paper we describe and analyze an algorithm for certain box constrained optimization problems that may have several local minima. A paradigm for these problems is one in which the function to be minimized is the sum of a simple function, such as a convex quadratic, and high frequency, low amplitude terms which cause local minima away from the global minimum of the simple function. Our me...

A generalization of Isakov's theorem ((13]) to admissible shapes that include screens with a Robin boundary condition (in which the impedance is also an unknown) is presented. We also establish a characterization that enables us to distinguish the far-eld of plane screens from others. Numerical results using a quasi-Newton method are presented.

Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g., count data), which leads to sparse tensors that can be modeled by sparse factor matrices. In this paper we investigate efficient techniques for computing an app...

Many researches attempt to improve the efficiency of the usual quasi-Newton (QN) methods by accelerating the performance of the algorithm without causing more storage demand. They aim to employ more available information from the function values and gradient to approximate the curvature of the objective function. In this paper we derive a new QN method of this type using a fourth order tensor m...

We consider conceptual optimization methods combining two ideas: the Moreau-Yosida regularization in convex analysis, and quasi-Newton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the local convergence properties of one of these approaches, which uses quasi-Newton updates of the o...