An Augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem

摘要: In this work, we present an Augmented Lagrangian algorithm for nonlinear semidefinite problems (NLSDPs), which is a natural extension of its consolidated counterpart in programming. This method works with two levels constraints; one that penalized and other kept within the subproblems. done to allow exploiting subproblem structure while solving it. The global convergence theory based on recent results regarding approximate Karush–Kuhn–Tucker optimality conditions NLSDPs, are stronger than usually employed Fritz John conditions. Additionally, approach problem covering given object fixed number balls minimum radius, where employ some convex algebraic geometry tools, such as Stengle’s Positivstellensatz variations, allows much more general model. Preliminary numerical experiments presented.