Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A genetic algorithm for the generalised assignment problem
Computers and Operations Research
On the projected subgradient method for nonsmooth convex optimization in a Hilbert space
Mathematical Programming: Series A and B
Error stability properties of generalized gradient-type algorithms
Journal of Optimization Theory and Applications
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Introduction to Linear Optimization
Introduction to Linear Optimization
An Incremental Gradient(-Projection) Method with Momentum Term and Adaptive Stepsize Rule
SIAM Journal on Optimization
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Incremental Subgradient Methods for Nondifferentiable Optimization
SIAM Journal on Optimization
A Heuristic Method for the Set Covering Problem
Operations Research
Survey: Covering problems in facility location: A review
Computers and Industrial Engineering
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The Lagrangean dual problem, with a non-differentiable convex objective function, is usually solved by using the subgradient method, whose convergence is guaranteed if the optimal value of the dual objective function is known. In practice, this optimal value is approximated by a previously computed bound. In this work, we combine the subgradient method with a different choice of steplength, based on the recently developed spectral projected gradient method, that does not require either exact or approximated estimates of the optimal value. We also add a momentum term to the subgradient direction that accelerates the convergence process towards global solutions. To illustrate the behavior of our new algorithm we solve Lagrangean dual problems associated with integer programming problems. In particular, we present and discuss encouraging numerical results for set covering problems and generalized assignment problems.