A projection-filter method for solving nonlinear complementarity problems

作者：Long Jun; Zeng Sanyun

来源：Applied Mathematics and Computation, 2010, 216(1): 300-307.

DOI：10.1016/j.amc.2010.01.063

• Nonlinear complementarity problem
• Filter method
• Josephy-Newton method
• Projection step
• Convergence

The Josephy-Newton method attacks nonlinear complementarity problems which consists of solving, possibly inexactly, a sequence of linear complementarity problems. Under appropriate regularity assumptions, this method is known to be locally (superlinearly) convergent. Utilizing the filter method, we presented a new globalization strategy for this Newton method applied to nonlinear complementarity problem without any merit function. The strategy is based on the projection-proximal point and filter methodology. Our linesearch procedure uses the regularized Newton direction to force global convergence by means of a projection step which reduces the distance to the solution of the problem. The resulting algorithm is globally convergent to a solution. Under natural assumptions, locally superlinear rate of convergence was established.

• 出版日期2010-3-1