Abstract Convexity and Augmented Lagrangians
Regina Sandra Burachik, Alex M. Rubinov · SIAM Journal on Optimization · 2007
The ultimate goal of this paper is to demonstrate that abstract convexity provides a natural language and a suitable framework for the examination of zero duality gap properties and exact multipliers of augmented Lagrangians. We study augmented Lagrangians in a very general setting and formulate the main definitions and facts describing the augmented Lagrangian theory in terms of abstract convexity tools. We illustrate our duality scheme with an application to stochastic semi‐infinite optimization.