A power penalty method for solving a nonlinear parabolic complementarity problem

A Singular Values Based Newton Method for Linear Complementarity Problems

“…The nonlinear penalized problems (1.2) corresponding to the linear complementarity problem (1.1), which its research has achieved good results. Wang [9] [10], Yang [11] and Li [12] [13]…”

An Interval Matrix Based Generalized Newton Method for Linear Complementarity Problems

“…In 2008, Yang [7] proved that solution to this penalized Equations (1.2) converged to that of the LCP at an exponential rate for a positive definite matrix case where the diagonal entries were positive and off-diagonal entries were not greater than zero. The same year, Wang and Huang [9] presented a penalty method for solving a complementarity problem involving a secondorder nonlinear parabolic differential operator, and defined a nonlinear parabolic partial differential equation (PDE) approximating the variational inequality using a power penalty term with a penalty constant 1 λ > , a power parameter k >0 and a smoothing parameter ε . And prove that the solution to the penalized PDE converges to that of the variational inequality in an appropriate norm at an arbitrary exponential rate of the form…”

A Superlinearly Convergent Method for a Class of Complementarity Problems with Non-Lipschitzian Functions

“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php as the reaction-diffusion problems [3,4], the nonlinear parabolic complementarity problem [21], and European and American option valuation [2,22]. In order to find a numerical solution for these problems, we can use a discretization method such as the central difference, the piecewise linear finite element, or a finite volume method [21,22] to reduce these problems into (1.1) or (1.2). Then a numerical solution of these problems is obtained by solving (1.1) or (1.2).…”