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
Chebyshev center based column generation
Discrete Applied Mathematics
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
Hi-index | 0.01 |
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 multi-depot vehicle scheduling instances show a great stabilizing and accelerating effect on the column generation method.