New variants of bundle methods
Mathematical Programming: Series A and B
A descent method with linear programming subproblems for nondifferentiable convex optimization
Mathematical Programming: Series A and B
Solving semidefinite quadratic problems within nonsmooth optimization algorithms
Computers and Operations Research
Discrete Mathematics
SIAM Journal on Optimization
Convergence of Proximal-Like Algorithms
SIAM Journal on Optimization
Computational Optimization and Applications
Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems
Transportation Science
A proximal trust-region algorithm for column generation stabilization
Computers and Operations Research
A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem
Operations Research
Comparison of bundle and classical column generation
Mathematical Programming: Series A and B
A proximal cutting plane method using Chebychev center for nonsmooth convex optimization
Mathematical Programming: Series A and B
Interior point stabilization for column generation
Operations Research Letters
Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment
INFORMS Journal on Computing
Stabilized branch-and-price for the rooted delay-constrained steiner tree problem
INOC'11 Proceedings of the 5th international conference on Network optimization
A shortest path-based approach to the multileaf collimator sequencing problem
Discrete Applied Mathematics
Transforming mathematical models using declarative reformulation rules
LION'05 Proceedings of the 5th international conference on Learning and Intelligent Optimization
Piecewise-quadratic Approximations in Convex Numerical Optimization
SIAM Journal on Optimization
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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Column generation algorithms are instrumental in many areas of applied optimization, where linear programs with an enormous number of columns need to be solved. Although successfully employed in many applications, these approaches suffer from well-known instability issues that somewhat limit their efficiency. Building on the theory developed for nondifferentiable optimization algorithms, a large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) augmented Lagrangian of the primal master problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, one can use piecewise-linear or quadratic functions that can be efficiently dealt with using off-the-shelf solvers. The practical effectiveness of this approach is demonstrated by extensive computational experiments on large-scale Vehicle and Crew Scheduling problems. Also, the results of a detailed computational study on the impact of the different choices in the stabilization term (shape of the function, parameters), and their relationships with the quality of the initial dual estimates, on the overall effectiveness of the approach are reported, providing practical guidelines for selecting the most appropriate variant in different situations.