Let Sˆ be a nonempty subset of Rn, and let f : Sˆ → R, g : Sˆ → Rm and h : Sˆ → Rp be given functions. Let the constraint set be nonempty. Let the functions f, g1,...,gm, h1,...,hp be differentiable...

Let Sˆ be a nonempty subset of Rn, and let f : Sˆ → R, g : Sˆ → Rm and h : Sˆ → Rp be given functions. Let the constraint set

be nonempty. Let the functions f, g1,...,gm, h1,...,hp be differentiable at some x¯ ∈ S. Let there be multipliers ui ≥ 0 (i ∈ I (x)) ¯ and vi ∈ R (i ∈ {1,...,p}) with

Let f be pseudoconvex at x¯, for every i ∈ I (x)¯ let gi be quasiconvex at x¯, for every i ∈ {1,...,p} with vi > 0 let hi be quasiconvex at x¯, and for every i ∈ {1,...,p} with vi <>