Superlinear Convergence of a Semismooth Newton Method for Some Optimization Problems with Applications to Control Theory
针对一类抽象优化问题提出半光滑牛顿法，在满足二阶充分最优条件和严格互补条件下证明其超线性收敛，并应用于椭圆和抛物型方程的控制问题。
In this paper, we formulate a semismooth Newton method for an abstract optimization problem and prove its superlinear convergence by assuming that the no-gap second order sufficient optimality condition and the strict complementarity condition are fulfilled at the local minimizer. Many control problems fit this abstract formulation. In particular, we apply this abstract result to distributed control problems of a semilinear elliptic equation, to boundary bilinear control problems associated with a semilinear elliptic equation, and to distributed control of a semilinear parabolic equation.