Optimality Conditions for Mathematical Programs with Orthogonality Type Constraints

Abstract We consider the class of mathematical programs with orthogonality type constraints. Orthogonality constraints appear by reformulating sparsity constraint via auxiliary binary variables and relaxing them afterwards. For a necessary optimality condition in terms T-stationarity is stated. The justification threefold. First, it allows to capture global structure Morse theory, i. e. deformation cell-attachment results are established. that, nondegeneracy for T-stationary points introduced shown hold generically. Second, we prove that Karush-Kuhn-Tucker Scholtes-type regularization converge This done under tailored linear independence qualification, which turns out be generic property too. Third, show applied relaxation constrained nonlinear optimization naturally leads its M-stationary points. Moreover, argue all this become degenerate.