A penalty method for a finite-dimensional obstacle problem with derivative constraints

作者：Wang Song^*

来源：Optimization Letters, 2014, 8(6): 1799-1811.

DOI：10.1007/s11590-013-0651-4

• Obstacle problem
• Gradient constraints
• Financial option pricing
• Variational inequality
• Penalty method
• Rate of convergence

We propose a power penalty method for an obstacle problem arising from the discretization of an infinite-dimensional optimization problem involving differential operators in both its objective function and constraints. In this method we approximate the mixed nonlinear complementarity problem (NCP) arising from the KKT conditions of the discretized problem by a nonlinear penalty equation. We then show the solution to the penalty equation converges exponentially to that of the mixed NCP. Numerical results will be presented to demonstrate the theoretical convergence rates of the method.

• 出版日期2014-8