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...

In this paper we construct C continuous piecewise quadratic hierarchical bases on Powell–Sabin triangulations of arbitrary polygonal domains in R. Our bases are of Lagrange type instead of the usual Hermite type and we prove that they form strongly stable Riesz bases for the Sobolev spaces Hs(Ω) with s ∈ (1, 5 2 ). Especially the case s = 2 is of interest, because we can use the corresponding h...

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...

The equilibrium chemical reactions taken place in a converter reactor of the Khorasan Petrochemical Ammonia plant was studied using the minimization of Gibbs free energy method. In the minimization of the Gibbs free energy function the Davidon– Fletcher–Powell (DFP) optimization procedure using the penalty terms in the well-defined objective function was used. It should be noted that in the DFP...

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...

We present well-balanced high-resolution finite volume schemes for simulating waves in the outer solar atmosphere. The schemes approximate the stratified MHD equations with an upwind discretization of the Godunov-Powell source term and a locally hydrostatic pressure reconstruction that preserves discrete steady states. The paper summarizes recent articles [4, 5, 6].

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...