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Role of copositivity in optimality criteria for nonconvex optimization problems

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Second-order necessary and sufficient conditions for local optimality in constrained optimization problems are discussed. For global optimality, a criterion recently developed by Hiriart-Urruty and Lemarechal is thoroughly examined in the case of concave quadratic problems and reformulated into copositivity conditions.

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Communicated by G. Leitmann

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Danninger, G. Role of copositivity in optimality criteria for nonconvex optimization problems. J Optim Theory Appl 75, 535–558 (1992). https://doi.org/10.1007/BF00940491

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Key Words

  • Copositive matrices
  • convex maximization problems
  • concave minimization
  • global optimality conditions