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 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...

Optimization Based Globally Convergent Methods for the Nonlinear Complementarity Problem

The nonlinear complementarity problem has been used to study and formulate various equilibrium problems including the traffic equilibrium problem, the spatial equilibrium problem and the Nash equilibrium problem. To solve the nonlinear complementarity problem, various iterative methods such as projection methods, linearized methods and Newton method have been proposed and their convergence resu...

A globally convergent incremental Newton method

Motivated by machine learning problems over large data sets and distributed optimization over networks, we develop and analyze a new method called incremental Newton method for minimizing the sum of a large number of strongly convex functions. We show that our method is globally convergent for a variable stepsize rule. We further show that under a gradient growth condition, convergence rate is ...

A Globally Convergent LP-Newton Method

We develop a globally convergent algorithm based on the LP-Newton method, which has been recently proposed for solving constrained equations, possibly nonsmooth and possibly with nonisolated solutions. The new algorithm makes use of linesearch for the natural merit function and preserves the strong local convergence properties of the original LP-Newton scheme. We also present computational expe...