Sufficient optimality criteria and duality for multiobjective variational problems with \(V\)-invexity
Recently, Jeyakumar and Mond introduced the concept of \(V\)-invexity. A vector of differentiable functions is said to be \(V\)-invex if each component function is invex with respect to some strictly positive multiple of \(\eta\). Here the concept of \(V\)-invexity (as well as \(V\)- pseudo-invexity and \(V\)-quasi-invexity) is defined for a vector of continuous functions \(f(t, x,\dot x)\). These concepts are then applied to obtain sufficiency and duality results for the continuous nonlinear multiobjective programming problem \[ V\text{-}\min\Biggl(\int^ T_ 0 f_ 1(t, x,\dot x) dt,\;\int^ T_ 0 f_ 2(t, x, \dot x)dt,\dots, \int^ T_ 0 f_ k(t, x, \dot x)dt\Biggr) \] subject to \(x(0)= \alpha\), \(x(T)= \beta\), \(g(t, x,\dot x)\leq 0\), \(0\leq t\leq T\), where \(V\)-min means find a weak minimum.
continuous nonlinear multiobjective programming
scientific article; zbMATH DE number 695827