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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

10.1007/s00338-015-1342-7

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1573-2916

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Existence and iterative algorithm of solutions for

Authors: Xie Ping Ding
Publish Date: 2011/05/17
Volume: 53, Issue: 3, Pages: 525-537
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Abstract

A new class of bilevel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in Banach spaces First an auxiliary generalized mixed equilibrium problem AGMEP to compute the approximate solutions of the generalized mixed equilibrium problems GMEP and bilevel generalized mixed equilibrium problems BGMEP involving setvalued mappings is introduced By using a minimax inequality the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions By using auxiliary principle technique new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP are suggested and analyzed The strong convergence of the iterative sequences generated by the algorithms are proved under quite mild assumptions These results are new and generalize some recent results in this field


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Other Papers In This Journal:

  1. On Slater’s condition and finite convergence of the Douglas–Rachford algorithm for solving convex feasibility problems in Euclidean spaces
  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. Vector equilibrium problems with elastic demands and capacity constraints
  14. Stability Index Method for Global Minimization
  15. Dynamic sample budget allocation in model-based optimization
  16. On an elliptic Kirchhoff-type problem depending on two parameters
  17. Some constraint qualifications for quasiconvex vector-valued systems
  18. Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part II—performance evaluation of draft tube model
  19. Global optimization of polynomial-expressed nonlinear optimal control problems with semidefinite programming relaxation
  20. A Lagrangian search method for the P -median problem
  21. Minimum vertex cover in ball graphs through local search
  22. Approximating zeros of monotone operators by proximal point algorithms

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