Augmented Lagrangian dual for nonconvex minimax fractional programs and proximal bundle algorithms for its resolution

Abstract

<p style='text-indent:20px;'>Based on augmented Lagrangian, we propose in this paper a new dual for inequality constrained nonconvex generalized fractional programs (GFP). We give duality results under quite weak assumptions. We associate with this dual program, parametric dual subproblems and establish duality results with the usual parametric primal ones. By taking advantage of the concavity of the parametric dual functions, we propose proximal bundle-like methods that approximately solve the parametric dual subproblems, to finally solve this dual program. For some problems, these method converge linearly.</p>