Duality for multiobjective fractional programming involving generalized \(\eta\)-bonvex functions
Considered is the following multiobjective fractional programming problem: \[ \hbox{Minimize}_{x\in X}\left({f_ 1(x)\over g_ 1(x)}, {f_ 2(x)\over g_ 2(x)}, \dots, {f_ t(x)\over g_ t(x)}\right),\leqno(P) \] subject to \(h(x)\geq 0\), \(l(x)=0\) where \(X\subseteq R^ n\), \(f_ i: X\to R\), \(g_ i: X\to R\) for \(i=1,2,\dots,t\), \(h:X\to R^ m\) and \(l:X\to R^ k\) are twice differentiable functions with \(f_ i(.)\geq 0\) and \(g_ i(.)>0\) for \(i=1,2,\dots,t\), and minimization entails obtaining efficient solutions. The author gives higher order duality results for problem \((P)\) in which the functions involved satisfy generalized \(\eta\)-bonvexity assumptions.
multiobjective fractional programming problem
scientific article; zbMATH DE number 14573