We analyze a technique for unconstrained minimization without derivatives. This stems from two theorems proved by M. J. D. Powell. A particular version, which we consider in detail, is related to the Jacobi process for finding the eigensystem of a symmetric matrix, and the two processes, although different, help to illuminate one another. We study convergence of the search directions to mutual ...

This paper presents a method to register a preoperative CT volume to a sparse set of intraoperative US slices. In the context of percutaneous renal puncture, the aim is to transfer a planning information to an intraoperative coordinate system. The spatial position of the US slices is measured by localizing a calibrated probe. Our method consists in optimizing a rigid 6 degree of freedom (DOF) t...

Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which call J-symmetric method. The is obtained by exploiting structure of second-order derivative objective function in problem. We show that Hessian estimation (as well as its inverse) can be updated rank...

Cuckoo search (CS) has been recently proposed as a population-based optimization algorithm and it is has so far been successfully applied in a variety of fields. An efficient hybrid cuckoo search algorithm (HCSA) based on Powell direct search method is proposed for solving constrained engineering design optimization problems. The inertia weight of Levy flights is introduced to balance the abili...

this article investigates the nonlinear, steady boundary layer flow and heat transfer of an incompressible eyring-powell non-newtonian fluid from an isothermal sphere with biot number effects. the transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference keller box technique. the influ...

Augmented Lagrangian algorithms are very popular tools for solving nonlinear programming problems. At each outer iteration of these methods a simpler optimization problem is solved, for which efficient algorithms can be used, especially when the problems are large. The most famous Augmented Lagrangian algorithm for minimization with inequality constraints is known as Powell-Hestenes-Rockafellar...

can in general only be found by an iterative process in which successively better, in some sense, approximations to the solution are computed. Of the methods available most rely on evaluating at each stage of the calculation a set of residuals and from these obtaining a correction to each element of the approximate solution. The most common way of doing this is to take each correction to be a s...

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a mi...

Cables have always been under consideration as a structural element because of important features such as large strength to weight ratios and long spans. Their equilibrium analysis is an important issue in this regard. But this analysis involves highly nonlinear equations arising from large deformations and material nonlinearity. Different methods have been under use for numerical analysis of s...