Abstract
In this paper, we analyse a local convergence of augmented Lagrangian method (ALM) for a class of nonlinear circular conic optimization problems. In light of the singular value decomposition, the Debreu theorem and the implicit function theorem, we prove that the sequence generated by ALM converges to a local minimizer in the linear convergence rate under the constraint nondegeneracy condition and the strong second-order sufficient condition, in which the ratio constant is proportional to 1 / τ , where τ is the associated penalty parameter with a given lower threshold. As a byproduct, we also derive explicit expressions of critical cone and its affine hull for the given nonlinear circular conic program.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have