On saddle points in nonconvex semi-infinite programming

  • Authors:

  • Francisco Guerra-Vázquez;Jan-J. Rückmann;Ralf Werner

  • Affiliations:

  • Escuela de Ciencias, San Andrés Cholula, Universidad de las Américas, Puebla, Puebla, México 72820;School of Mathematics, The University of Birmingham, Birmingham, UK B15 2TT;Munich University of Applied Sciences, Munich, Germany 80335

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2012

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Abstract

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems.