This work deals with convergence to points satisfying the weak second-order necessary optimality conditions of a second-order safeguarded augmented Lagrangian method from the literature. To this end, we propose a new second-order sequential optimality condition that is, in a certain way, based on the iterates generated by the algorithm itself. This also allows us to … Read more
In [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez C., Weak notions of nondegeneracy in nonlinear semidefinite programming, arXiv:2012.14810, 2020] the classical notion of nondegeneracy (or transversality) and Robinson’s constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely, its eigendecomposition. This allows formulating the … Read more
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global convergence proof of a class of algorithms to stationary points without assuming neither uniqueness of the Lagrange multiplier nor boundedness of the Lagrange … Read more
In second-order algorithms, we investigate the relevance of the constant rank of the full set of active constraints in ensuring global convergence to a second-order stationary point. We show that second-order stationarity is not expected in the non-constant rank case if the growth of the so-called tangent multipliers, associated with a second-order complementarity measure, is … Read more