A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit the piece-wise linear nature of the dual problem. The second part of the paper applies the previous result to acceleration of convex minimization problems, and...

A Hessian matrix in full waveform inversion (FWI) is difficult to compute directly because of high computational cost and an especially large memory requirement. Therefore, Newton-like methods are rarely feasible in realistic large-size FWI problems. We modify the quasi-Newton BFGS method to use a projected Hessian matrix that reduces both the computational cost and memory required, thereby mak...

This paper shows how various limited-memory quasi-Newton large-scale unconstrained minimization methods can be used to speed up the location of global minima of potential energy surfaces related to the structures of mixed Ar-Xe clusters. Both a simulated annealing method and a finitetemperature lattice-based Monte Carlo method are accelerated by the various quasi-Newton limitedmemory methods wh...

At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe automatic preconditioning techniques for iterative methods for solving such sequences of systems by maintaining an estimate of the inverse system matrix. We up...

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...