Optimality Conditions and Duality for Nonsmooth Fractional Continuous-Time Problems

Saddle-point type optimality criteria, duality and a new approach for solving nonsmooth fractional continuous-time programming problems

“…One of the earliest papers in the field of fractional continuous-time programming is the paper by Zalmai [21]. For recent results in this field, the reader is also referred to [7,22,9,12,14,13,11,15,10]. In [22], optimality conditions were obtained for a class of nonsmooth fractional programming problems with Volterratype integral inequality.…”

“…One of the main tools in [7,21], was a generalized Gordan's Transposition Theorem in the continuous-time context (see [19]). However, it is widely known that the vast majority of literature, produced in the field of continuous-time programming, also makes use of the Gordan's Transposition Theorem.…”

“…In [7], the authors have established optimality criteria and duality results for the nonsmooth fractional continuous-time problem, with inequality constraints where the objective and inequality constraint functions are locally Lipschitz functions, but that article used the invalid result from [3] (see [1]). In fact, in [3] the fundamental tool was the Gordan's Transposition Theorem stated in [19], but that theorem was questioned in [1].…”