The essence of invexity

  title={The essence of invexity},
  author={D. H. Martin},
  journal={Journal of Optimization Theory and Applications},
  • D. H. Martin
  • Published 1 September 1985
  • Mathematics
  • Journal of Optimization Theory and Applications
AbstractThe notion of invexity was introduced into optimization theory by Hanson in 1981 as a very broad generalization of convexity. A smooth mathematical program of the form minimizef(x), subject tog(x) ≦ 0, isx ∈D ⊑ ℝninvex if there exists a function η:D ×D → ℝn such that, for allx, u ∈D, $$\begin{gathered} f(x) - f(u) - f'(u)n(x,u) \geqq 0, \hfill \\ g(x) - g(u) - g'(u)n(x,u) \geqq 0. \hfill \\ \end{gathered}$$ The convex case corresponds of course to η(x, u)≡x−u; but, as Hanson showed… Expand
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