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On sensitivity in optimal control problems

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Abstract

Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.

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Communicated by M. R. Hestenes

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Peterson, D.W. On sensitivity in optimal control problems. J Optim Theory Appl 13, 56–73 (1974). https://doi.org/10.1007/BF00935609

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Key Words

  • Sensitivity analysis
  • control theory
  • mathematical programming
  • method of multipliers
  • Banach spaces