Active‐set Newton methods for mathematical programs with vanishing constraints

Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious difficulties in theoretical and numerical treatment of these problems. In this work, we suggest several globalization strategies for the active‐set Newton‐type methods developed earlier by the authors for this problem class, preserving superlinear convergence rate of these methods under weak assumptions. Preliminary numerical results demonstrate that our approach is rather promising and competitive with respect to the existing alternatives.