A geometric framework for nonconvex optimization duality using augmented lagrangian functions

Authors:
Angelia Nedich;Asuman Ozdaglar
Affiliations:
Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, USA;Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, USA
Venue:
Journal of Global Optimization
Year:
2008

Citing 4
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Abstract

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems. Using the primal function of a constrained optimization problem, we apply our results both in the analysis of duality schemes constructed using augmented Lagrangian functions, and in establishing necessary and sufficient conditions for the convergence of penalty methods.