First, a class of comprehensive higher order exponential type generalized B-(b, ρ, η, ω, θ, p̃, r̃, s̃)-invexities is introduced, which encompasses most of the existing generalized invexity concepts in the literature, including the Antczak type first order B-(b, η, p̃, r̃)-invexities as well as the Zalmai type (α, β, γ, η, ρ, θ)-invexities, and then a wide range of parametrically sufficient optimali...

The sum of a fractional program is a nonconvex optimization problem in the field of fractional programming and it is difficult to solve. The development of research is restricted to single objective sums of fractional problems only. The branch and bound methods/algorithms are developed in the literature for this problem as a single objective problem. The theoretical and algorithmic development ...

*Correspondence: [email protected] 1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia 2Permanent address: Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Full list of author information is available at the end of the article Abstract This paper is devoted to study interval-valued optimization p...

Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems...

* Correspondence: drizhar@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Full list of author information is available at the end of the article Abstract In this article, we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution t...

let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...