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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

10.1016/0305-4179(77)90135-8

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1573-2916

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Global optimization of polynomialexpressed nonlin

Authors: Takeshi Tsuchiya
Publish Date: 2011/10/21
Volume: 54, Issue: 4, Pages: 831-854
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Abstract

In this paper we propose a new deterministic global optimization method for solving nonlinear optimal control problems in which the constraint conditions of differential equations and the performance index are expressed as polynomials of the state and control functions The nonlinear optimal control problem is transformed into a relaxed optimal control problem with linear constraint conditions of differential equations a linear performance index and a matrix inequality condition with semidefinite programming relaxation In the process of introducing the relaxed optimal control problem we discuss the duality theory of optimal control problems polynomial expression of the approximated value function and sumofsquares representation of a nonnegative polynomial By solving the relaxed optimal control problem we can obtain the approximated global optimal solutions of the control and state functions based on the degree of relaxation Finally the proposed global optimization method is explained and its efficacy is proved using an example of its application

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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. 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. 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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