New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limitedmemory BFGS using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. T...

An algorithm for solving large-scale nonlinear' programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable quasi-Newton methods for handling the nonlinearities. A general-purpose production code (MINOS) is described, along with computational experience on a wide variety of problems.

Full Waveform Inversion (FWI) methods use generally gradient based method, such as the nonlinear conjugate gradient method or more recently the l-BFGS quasi-Newton method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framewo...

We present a novel optimization-based algorithm for articulated body dynamics simulation. We formulate the governing equations of rigid body dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. We also extend our framework to handle joint limits, control forces/torques, fluid drag forces, and frictional contact forces. Our ref...

In this paper, a partially asynchronous block Broyden method is presented for solving nonlinear systems of equations of the form F(x)= 0. Sufficient conditions that guarantee its local convergence are given. In particular, local convergence is shown when the Jacobian F'(x*) is an H-matrix, where x* is the zero point o f F . The results are extended to Schubert's method. A connection with discre...

This paper uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstraiend optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but increase their c...

The position information is becoming more and more important for application in WSNs. So aiming at the location problem, the paper proposes a localization algorithm based on PSO (particle swarm optimization) and Quasi-Newton algorithm, which use PSO to get a satisfying value and then use it as the initial value of Quasi-Newton algorithm to iterate. The simulation experiments are carried out. Th...

When the computation of efficient preconditioners for individual linear systems of a sequence is expensive, significant reduction of costs can be achieved by updating previous preconditioners. For large and sparse systems, this has been done, among others, by recycling subspaces when using a Krylov subspace method [3], by means of small rank updates when applying Quasi-Newton methods [2] or wit...

The quasi-Newton strategy presented in this paper preserves one of the most important features of the stabilized Sequential Quadratic Programming method, the local convergence without constraint qualifications assumptions. It is known that the primal-dual sequence converges quadratically assuming only the second-order sufficient condition. In this work, we show that if the matrices are updated ...

We address the solution of convex constrained nonlinear systems by new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivativefree and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of th...