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Existence theorems for optimization problems concerning linear, hyperbolic partial differential equations without convexity conditions

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Abstract

Integral representations are obtained for solutions of a Darboux problem in a rectangle and used to prove Neustadt-type existence theorems for optimal control problems with trajectories satisfying linear, hyperbolic partial differential equations with Darboux-type boundary data. The proof bears on the fact that, in this situation, for each generalized solution, there is a usual solution where the functional takes the same value.

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Additional information

This work was done in the framework of Research Project AFOSR-69-1662. The author is greatly indebted to Professor L. Cesari for his valuable guidance and constant encouragement during the writing of this paper.

Communicated by L. Cesari

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Suryanarayana, M.B. Existence theorems for optimization problems concerning linear, hyperbolic partial differential equations without convexity conditions. J Optim Theory Appl 19, 47–61 (1976). https://doi.org/10.1007/BF00934051

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Key Words

  • Existence theorems
  • linear systems
  • Green's functions
  • hyperbolic partial differential equations
  • multidimensional control problems
  • relaxed solutions
  • convexity