Convex Functions with Unbounded Level Sets and Applications to Duality Theory
A. Auslender, Roberto Cominetti, J. P. Crouziex · SIAM Journal on Optimization · 1993
A class of convex functions with unbounded level sets but good behavior at infinity [Analyse non-linéaire, Gauthier-Villars, Paris, 1989, pp. 101–122] is investigated. Characterizations and properties are given. The results are then applied to studying sequential approximation schemes for optimization problems and to duality theory, when the involved functions have unbounded level sets. In particular, the convergence properties of stationary sequences for the dual of a convex program are studied, and methods for associating with it a primal sequence converging to a solution of the primal problem are demonstrated.