A globally convergent BFGS method for nonlinear monotone equations without any merit functions

A globally convergent BFGS method for nonlinear monotone equations without any merit functions

Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically ...

A Truly Globally Convergent Newton-Type Method for the Monotone Nonlinear Complementarity Problem

A Truly Globally Convergent Newton-type Method for the Monotone Nonlinear Complementarity

The Josephy-Newton method for solving a nonlinear complementarity problem consists of solving, possibly inexactly, a sequence of linear complementarity problems. Under appropriate regularity assumptions, this method is known to be locally (superlinearly) convergent. To enlarge the domain of convergence of the Newton method, some globalization strategy based on a chosen merit function is typical...

A new backtracking inexact BFGS method for symmetric nonlinear equations

A BFGS method, in association with a new backtracking line search technique, is presented for solving symmetric nonlinear equations. The global and superlinear convergences of the given method are established under mild conditions. Preliminary numerical results show that the proposed method is better than the normal technique for the given problems. c © 2007 Elsevier Ltd. All rights reserved.

A Globally Convergent Linearly Constrained Lagrangian Method for Nonlinear Optimization

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be reliable from arbitrary starting points. The well known example MINOS has proven effective on many large problems. Its success motivates us to propose a glo...