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Discretization methods for the solution of semi-infinite programming problems


In the first part of this paper, we prove the convergence of a class of discretization methods for the solution of nonlinear semi-infinite programming problems, which includes known methods for linear problems as special cases. In the second part, we modify and study this type of algorithms for linear problems and suggest a specific method which requires the solution of a quadratic programming problem at each iteration. With this algorithm, satisfactory results can also be obtained for a number of singular problems. We demonstrate the performance of the algorithm by several numerical examples of multivariate Chebyshev approximation problems.

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Communicated by E. Polak

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Reemtsen, R. Discretization methods for the solution of semi-infinite programming problems. J Optim Theory Appl 71, 85–103 (1991).

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Key Words

  • Nonlinear programming
  • semi-infinite programming
  • discretization of semi-infinite programming problems
  • Chebyshev approximation