In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Ne...

We show how the quasi-Newton least squares method (QN-LS) relates to Krylov subspace methods in general and to GMRes in particular.

The problem of minimizing an objective that can be written as the sum of a set of n smooth and strongly convex functions is challenging because the cost of evaluating the function and its derivatives is proportional to the number of elements in the sum. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and incremental methods that have a cost per iterat...

Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance [e.g., [8]]. In addition, most modern optimization libraries house a quasi-Newt...

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

A variable parametrization scheme is developed and demonstrated for shape optimization using quasi-Newton methods. The scheme performs adaptive parametrization refinement while preserving the approximate Hessian of the shape optimization problem and enables free-form shape design using quasi-Newton optimization methods. Using a Bspline parametrization, the scheme is validated using a 1-D shape ...