Necessary and sufficient optimality conditions are obtained under higher order strongly convexity for Lipschitz functions.
These concepts were compared to one another and were grouped under higher order, more abstract concepts (Corbin and Strauss 2008).
Subsequently, Bhatia [12] considered the notion of strict minimizer of order m for a multiobjective optimization problem and established only optimality for the concept of strict minimizer of order m under higher order strong convexity for Lipschitz functions.
The approach is derived assuming small damping and involves not only the diagonal terms of the modal damping matrix, but also the off-diagonal terms, which appear under higher order.
The codes were then "grouped together under higher order headings".
Nested themes were identified under higher order themes.
Subsequently, the generated list of categories was organized under higher order headings, creating so-called "generic categories".
Simulation results show that the resonance can be eliminated under high-order-frequency excitation and may happen when the excitation frequency is close to the first-order water sloshing frequency.
Further, duality results are obtained under higher-order ((F,alpha,rho,d -convexity.
Weak, strong and converse duality theorems under higher-order K- ( F, α, ρ, d ) -convexity assumptions have also been established.
In Chen [2], multiobjective fractional problem and its duality theorems have been considered under higher-order ((F,alpha,rho,d -convexity.
