A Lagrangian column-generation procedure is developed which retains the original problem functions for column generation but uses transformed penalty functions in the Lagrangian optimization. The class of penalty functions considered maintains the original order of differentiability and often...

The dilemma of when to cease analysis of a subproblem and go on to the next subproblem in convex programming is an especially difficult one. This paper views convex programming as an extension of linear programming and focuses attention on the analysis of a given subproblem. Specifically, if K =...