A smoothing-regularization approach to mathematical programs with vanishing constraints

作者：Achtziger Wolfgang^*; Hoheisel Tim; Kanzow Christian

来源：Computational Optimization and Applications, 2013, 55(3): 733-767.

DOI：10.1007/s10589-013-9539-6

• Mathematical programs with vanishing constraints
• Mathematical programs with equilibrium constraints
• Smoothing method
• Regularization method
• Global convergence

We consider a numerical approach for the solution of a difficult class of optimization problems called mathematical programs with vanishing constraints. The basic idea is to reformulate the characteristic constraints of the program via a nonsmooth function and to eventually smooth it and regularize the feasible set with the aid of a certain smoothing- and regularization parameter t %26gt; 0 such that the resulting problem is more tractable and coincides with the original program for t=0. We investigate the convergence behavior of a sequence of stationary points of the smooth and regularized problems by letting t tend to zero. Numerical results illustrating the performance of the approach are given. In particular, a large-scale example from topology optimization of mechanical structures with local stress constraints is investigated.

• 出版日期2013-7