Trust Region Methods
This chapter discusses Trust-Region Mewthods for General Constained Optimization and Systems of Nonlinear Equations and Nonlinear Fitting, and some of the methods used in this chapter dealt with these systems.
CUTE: constrained and unconstrained testing environment
The scope and functionality of a versatile environment for testing small- and large-scale nonlinear optimization algorithms, and tools to assist in building an interface between this input format and other optimization packages are discussed.
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank, an algorithm by Nesterov and Polyak and a proposal by Weiser et al.
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
This book, which is concerned with algorithms for solving large-scale non-linear optimization problems, is the only complete source of documentation for the software package Lancelot and will mainly…
A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds
The global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems are considered. In such methods, simple bound constraints are treated…
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
A new version of CUTE, now known as CUTEr, is presented, which includes reorganisation of the environment to allow simultaneous multi-platform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and entirely automated installation procedure for unix systems.
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity
The approach is more general in that it allows the cubic model to be solved only approximately and may employ approximate Hessians, and the orders of these bounds match those proved for Algorithm 3.3 of Nesterov and Polyak which minimizes the cubicmodel globally on each iteration.
Solving the Trust-Region Subproblem using the Lanczos Method
The key is to observe that the trust-region problem within the currently generated Krylov subspace has a very special structure which enables it to be solved very efficiently.
SIAM Journal on Optimization
The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear…
CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization
These updated versions of the constrained and unconstrained testing environment and its accompanying SIF decoder feature dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a revised installation procedure integrated with GALAHAD.