Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
A generalization of Polyak's convergence result for subgradient optimization
Mathematical Programming: Series A and B
Nondifferentiable optimization
Optimization
Variable target value subgradient method
Mathematical Programming: Series A and B
A global approach to crew-pairing optimization
IBM Systems Journal
SIAM Journal on Control and Optimization
A Lagrangian-based heuristic for large-scale set covering problems
Mathematical Programming: Series A and B - Special issue on computational integer programming
The Efficiency of Ballstep Subgradient Level Methods for Convex Optimization
Mathematics of Operations Research
A Heuristic Method for the Set Covering Problem
Operations Research
An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow
An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow
Selected Topics in Column Generation
Operations Research
Vehicle Routing and Staffing for Sedan Service
Transportation Science
A dual ascent procedure for the set partitioning problem
Discrete Optimization
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We deal with the linear programming relaxation of set partitioning problems arising in airline crew scheduling. Some of these linear programs have been extremely difficult to solve with the traditional algorithms. We have used an extension of the subgradient algorithm, the volume algorithm, to produce primal solutions that might violate the constraints by at most 2%, and that are within 1% of the lower bound. This method is fast, requires minimal storage, and can be parallelized in a straightforward way.