On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
Convergence rate analysis of nonquadratic proximal methods for convex and linear programming
Mathematics of Operations Research
A descent method with linear programming subproblems for nondifferentiable convex optimization
Mathematical Programming: Series A and B
Proximal Minimization Methods with Generalized Bregman Functions
SIAM Journal on Control and Optimization
Discrete Mathematics
SIAM Journal on Optimization
A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem
Operations Research
Dual-Optimal Inequalities for Stabilized Column Generation
Operations Research
On the choice of explicit stabilizing terms in column generation
Discrete Applied Mathematics
Stabilized branch-and-price for the rooted delay-constrained steiner tree problem
INOC'11 Proceedings of the 5th international conference on Network optimization
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This paper proposes a generalization of the proximal point algorithm using both penalty and trust-region concepts. Finite convergence is established while assuming the trust regions are of full dimension and never shrink to a single point. The approach is specialized to the cutting plane/column generation context. The resulting algorithm ensures convergence to a pair of primal and dual optimal solutions. Computational experiments carried over multidepot vehicle scheduling instances show a great stabilizing and accelerating effect on the column generation method.