Generalized -invexity and generalized -invariant-monotonicity

✍ Scribed by N. Behera; C. Nahak; S. Nanda

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 218 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.02.004

✦ Synopsis

In this paper several kinds of (ρ, θ)-η-invariant-monotone functions and generalized (ρ, θ)-η-invariant-monotone functions are considered. For a given Frechet differentiable function f, ∇ f (gradient of f ), (ρ, θ)-η-invariant-monotonicity of ∇ f is related to (ρ, θ)-η-invexity of f . It is also shown that (ρ, θ)-η-invariant-monotonicity and generalized (ρ, θ)-η-invariant-monotonicity are proper generalizations of invariant-monotonicity and generalized invariant-monotonicity.