Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Lagrangean decomposition: A model yielding stronger lagrangean bounds
Mathematical Programming: Series A and B
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Variable metric bundle methods: from conceptual to implementable forms
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Class Steiner trees and VLSI-design
Discrete Applied Mathematics - Special volume on VLSI
An Implementation of Shor's r-Algorithm
Computational Optimization and Applications
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A note on the generalized Steiner tree polytope
Discrete Applied Mathematics
Limited Memory Space Dilation and Reduction Algorithms
Computational Optimization and Applications
Decomposing Matrices into Blocks
SIAM Journal on Optimization
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Local search algorithms for the k-cardinality tree problem
Discrete Applied Mathematics
Strong lower bounds for the prize collecting Steiner problem in graphs
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem
Computers and Operations Research
Lagrangian duality applied to the vehicle routing problem with time windows
Computers and Operations Research
New metaheuristic approaches for the edge-weighted k-cardinality tree problem
Computers and Operations Research
A variable target value method for nondifferentiable optimization
Operations Research Letters
Algorithmic expedients for the Prize Collecting Steiner Tree Problem
Discrete Optimization
Tight compact models and comparative analysis for the prize collecting Steiner tree problem
Discrete Applied Mathematics
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We propose a generalized version of the Prize Collecting Steiner Tree Problem (PCSTP), which offers a fundamental unifying model for several well-known $\mathcal{NP}$ -hard tree optimization problems. The PCSTP also arises naturally in a variety of network design applications including cable television and local access networks. We reformulate the PCSTP as a minimum spanning tree problem with additional packing and knapsack constraints and we explore various nondifferentiable optimization algorithms for solving its Lagrangian dual. We report computational results for nine variants of deflected subgradient strategies, the volume algorithm (VA), and the variable target value method used in conjunction with the VA and with a generalized Polyak---Kelley cutting plane technique. The performance of these approaches is also compared with an exact stabilized constraint generation procedure.