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On invexity-type nonlinear programming problems

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Abstract

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, ϕ)-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.

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Additional information

The author wishes to thank the referee for helpful comments.

Communicated by, R. A. Tapia

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Xu, Z.K. On invexity-type nonlinear programming problems. J Optim Theory Appl 80, 135–148 (1994). https://doi.org/10.1007/BF02196597

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Key Words

  • Fritz John points
  • Kuhn-Tucker points
  • saddle points
  • generalized invexity
  • (h, ϕ)-convex programming
  • generalized fractional programming