An inversion procedure for obtaining speeds, attenuation, densities, and thicknesses for a layered medium is described. The inversion is carried out using the least-squares technique and the forward modeling is based on SAFARI. The optimization is a hybrid method combining the global genetic algorithms and the local Gauss-Newton method. This is done by taking several gradient steps between each...

We propose a curvilinear search for nonlinear systems of equations and path-following methods that are very nonlinear with the dominant part in the tangent space. The curvilinear search is very easy to implement and should be used with the (Gauss-)Newton method. At the cost of one function evaluation the curvature along the search direction can be reduced. For zero residual nonlinear least squa...

We investigate Newton-type optimization methods for solving piecewise linear systems (PLS) with non-degenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem which is useful to model several learning and optimization problems. In this paper, we propose an effective damped Newton method, namely PLSDN, to find the exact solution ...

Tracking of a moving target by uncalibrated model independent visual servo control is achieved by developing a new \dynamic" quasi-Newton approach. Model independent visual servo control is de ̄ned as using visual feedback to control a robot without precisely calibrated kinematic and camera models. The control problem is formulated as a nonlinear least squares optimization. For the moving target...

A mathematical model for the computation of the phase equilibrium and gas-particle partitioning in atmospheric organic aerosols is presented. The thermodynamic equilibrium is determined by the global minimum of the Gibbs free energy under equality and inequality constraints for a system that involves one gas phase and many liquid phases. A primal-dual interior-point algorithm is presented for t...

We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machin...

Numerous scientific applications across a variety of fields depend on box-constrained convex optimization. Box-constrained problems therefore continue to attract research interest. We address box-constrained (strictly convex) problems by deriving two new quasi-Newton algorithms. Our algorithms are positioned between the projected-gradient [J. B. Rosen, J. SIAM, 8(1), 1960, pp. 181–217], and pro...

Many problems in science and engineering must solve nonlinear necessary conditions for defining meaningful solutions. For example, a standard problem in optimization involves solving for the roots of nonlinear functions defined by f(x) = 0, where x is the unknown variable. Classically one develops a first-order Taylor series model which provides the necessary condition that must be iteratively ...

Nonlinear least squares (NLS) problems arise in many applications. The common solvers require to compute and store the corresponding Jacobian matrix explicitly, which is too expensive for large problems. In this paper, we propose an effective Jacobian free method especially for large NLS problems because of the novel combination of using automatic differentiation for J(x)v and J (x)v along with...