An augmented Lagrangian method for optimization problems with structured geometric constraints

Abstract This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for solution optimization problems with geometric constraints. Specifically, we study situations where parts constraints are nonconvex possibly complicated, but allow a fast computation projections onto this set. Typical problem classes which satisfy requirement disjunctive (like complementarity or cardinality constraints) as well over sets matrices have additional rank The key idea behind our keep these complicated explicitly in penalize only remaining by function. resulting subproblems then solved aid problem-tailored nonmonotone projected gradient method. corresponding convergence theory allows inexact subproblems. Nevertheless, overall algorithm computes so-called Mordukhovich-stationary points original under mild asymptotic regularity condition, generally weaker than most respective available constraint qualifications. Extensive experiments addressing complementarity- cardinality-constrained semidefinite reformulation MAXCUT visualize power approach.