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 experiments on a set of generalized Nash equilibrium problems, and a comparison of our approach with the previous hybrid globalization employing the potential reduction method. © 2016 Society for Industrial and Applied Mathematics

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 experiments on a set of generalized Nash equilibrium problems, and a comparison of our approach with the previous hybrid globalization employing the potential reduction method. © 2016 Society for Industrial and Applied Mathematics

A globally convergent LP-Newton method for piecewise smooth constrained equations: escaping nonstationary accumulation points

The LP-Newton method for constrained equations, introduced some years ago, has powerful properties of local superlinear convergence, covering both possibly nonisolated solutions and possibly nonsmooth equation mappings. A related globally convergent algorithm, based on the LP-Newton subproblems and linesearch for the equation’s infinity norm residual, has recently been developed. In the case of smooth equations, global convergence of this algorithm to B-stationary points of the residual over the constraint set has been shown, which is a natural result: nothing better should generally be expected in variational settings. However, for the piecewise smooth case only a property weaker than B-stationarity could be guaranteed. In this paper, we develop a procedure for piecewise smooth equations that avoids undesirable accumulation points, thus achieving the intended property of B-stationarity. © 2017, Springer Science+Business Media, LLC

A globally convergent LP-Newton method for piecewise smooth constrained equations: escaping nonstationary accumulation points

The LP-Newton method for constrained equations, introduced some years ago, has powerful properties of local superlinear convergence, covering both possibly nonisolated solutions and possibly nonsmooth equation mappings. A related globally convergent algorithm, based on the LP-Newton subproblems and linesearch for the equation’s infinity norm residual, has recently been developed. In the case of smooth equations, global convergence of this algorithm to B-stationary points of the residual over the constraint set has been shown, which is a natural result: nothing better should generally be expected in variational settings. However, for the piecewise smooth case only a property weaker than B-stationarity could be guaranteed. In this paper, we develop a procedure for piecewise smooth equations that avoids undesirable accumulation points, thus achieving the intended property of B-stationarity. © 2017, Springer Science+Business Media, LLC