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 ...

We develop a Newton method for the optimization of trajectory functionals. Through the use of a trajectory tracking nonlinear projection operator, the dynamically constrained optimization problem is converted into an unconstrained problem, making many aspects of the algorithm rather transparent. Examples: first and second order optimality conditions, search direction and step length calculation...

In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact (or inexact) line search. It turns out that in some situations, the proposed algorithm is equivalent to a class of SR1 (identity minus rank 1) proximal quas...

A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given. The methods are based on a positive definite inverse Hessian approximation in the form of the sum of identity matrix and two low rank matrices, obtained by the standard scaled Broyden class update. To reduce the rank of matrices, various projections are used. Numerical experience is e...

This paper describes a reduced quasi-Newton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced Hessian of the Lagrangian. A new approach is proposed in this paper. The idea is to search for the next itera...

Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are d...

Neural Network Learning algorithms based on Conjugate Gradient Techniques and Quasi Newton Techniques such as Broyden, DFP, BFGS, and SSVM algorithms require exact or inexact line searches in order to satisfy their convergence criteria. Line searches are very costly and slow down the learning process. This paper will present new Neural Network learning algorithms based on Hoshino's weak line se...

We present a new matrix-free method for the computation of the negative curvature direction in large scale unconstrained problems. We describe a curvilinear method which uses a combination of a quasi-Newton direction and a negative curvature direction. We propose an algorithm for the computation of the search directions which uses information of two specific L-BFGS matrices in such a way that a...

This paper proposes an implementable proximal quasi-Newton method for minimizing a nondifferentiable convex function f in <n . The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point p(xk) of xk to define a vk ∈ ∂ k f(p(xk))with k ≤ α‖vk‖,where α is a constant. The method monitors the reduction in the value ...

The classical trust-region method for unconstrained minimization can be augmented with a line search that finds a point that satisfies the Wolfe conditions. One can use this new method to define an algorithm that simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian of the objective function. This new algorithm has s...