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Title of Journal: J Glob Optim

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Abbravation: Journal of Global Optimization

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Springer US

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DOI

10.1002/ir.10407

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1573-2916

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A Lagrangian search method for the Emphasis Type=

Authors: Joshua Q Hale Enlu Zhou Jiming Peng
Publish Date: 2016/11/01
Volume: 69, Issue: 1, Pages: 137-156
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Abstract

In this paper we propose a novel algorithm for solving the classical Pmedian problem The essential aim is to identify the optimal extended Lagrangian multipliers corresponding to the optimal solution of the underlying problem For this we first explore the structure of the data matrix in Pmedian problem to recast it as another equivalent global optimization problem over the space of the extended Lagrangian multipliers Then we present a stochastic search algorithm to find the extended Lagrangian multipliers corresponding to the optimal solution of the original Pmedian problem Numerical experiments illustrate that the proposed algorithm can effectively find a global optimal or very good suboptimal solution to the underlying Pmedian problem especially for the computationally challenging subclass of Pmedian problems with a large gap between the optimal solution of the original problem and that of its Lagrangian relaxationThe research of the first two authors are supported by the National Science Foundation Graduate Research Fellowship under Grant 0946809 the National Science Foundation under Grant CMMI1413790 Air Force office of Scientific Research under Grant FA95501410059 and AFRL Mathematical Modeling and Optimization Institute The research of the last author is supported by NSF Award CMMI1131690 Any opinions findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation the Air Force office of Scientific Research and the AFRL Mathematical Modeling and Optimization Institute

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  2. Iterative algorithms for variational inequality and equilibrium problems with applications
  3. Efficient Nash equilibria on semilattices
  4. Global optimal solutions to a class of quadrinomial minimization problems with one quadratic constraint
  5. Global search perspectives for multiobjective optimization
  6. Necessary optimality conditions for a set-valued fractional extremal programming problem under inclusion constraints
  7. Rigorous filtering using linear relaxations
  8. On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation
  9. Low dimensional simplex evolution: a new heuristic for global optimization
  10. A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks
  11. Variational inclusions problems with applications to Ekeland’s variational principle, fixed point and optimization problems
  12. A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints
  13. Existence and iterative algorithm of solutions for a class of bilevel generalized mixed equilibrium problems in Banach spaces
  14. Vector equilibrium problems with elastic demands and capacity constraints
  15. Stability Index Method for Global Minimization
  16. Dynamic sample budget allocation in model-based optimization
  17. On an elliptic Kirchhoff-type problem depending on two parameters
  18. Some constraint qualifications for quasiconvex vector-valued systems
  19. Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part II—performance evaluation of draft tube model
  20. Global optimization of polynomial-expressed nonlinear optimal control problems with semidefinite programming relaxation
  21. Minimum vertex cover in ball graphs through local search
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