This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasi-Newton method in the corrector procedure, and an application of the conjugate gradient method with an effective preconditioning matrix ...

Historical Development of the BFGS Secant Method and Its Characterization Properties by Joanna Maria Papakonstantinou The BFGS secant method is the preferred secant method for finite-dimensional unconstrained optimization. The first part of this research consists of recounting the historical development of secant methods in general and the BFGS secant method in particular. Many people believe t...

We compare the performance of several robust large-scale minimization algorithms for the unconstrained minimization of an ill-posed inverse problem. The parabolized Navier-Stokes equations model was used for adjoint parameter estimation. The methods compared consist of two versions of the nonlinear conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [15...

This paper addresses the equal circle packing problem, and proposes an efficient quasi-physical algorithm(EQPA). EQPA is based on an improved BFGS algorithm and a new basin hopping strategy. Starting form a random initial pattern, we use the modified BFGS algorithm to reach a local minimum pattern. The modified BFGS algorithm fully utilizes the neighborhood information and considerably speeds u...

This paper proposes a BFGS-SQP method for linearly constrained optimization where the objective function f is only required to have a Lipschitz gradient. The KKT system of the problem is equivalent to a system of nonsmooth equations F(v) = 0. At every step a quasi-Newton matrix is updated if kF(v k)k satisses a rule. This method converges globally and the rate of convergence is su-perlinear whe...

The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is...

In this paper we consider a number of real world case studies using an automatic design optimisation system called Nimrod/O. The case studies include a photochemical pollution model, two different simulations of the strength of a mechanical part and the radio frequency properties of a ceramic bead. In each case the system is asked to minimise an objective function that results from the executio...