Fractional semi-infinite programming problems: optimality conditions and duality via tangential subdifferentials

Abstract

In this paper, we have focused on a multi-objective fractional semi-infinite programming problems in which the constraints and objective functions are tangentially convex. A result has been established to find the tangential subdifferential of a fractional function, assuming the numerator and the negative of the denominator being tangentially convex functions. With this, optimality conditions have been derived using a non-parametric approach under \(\digamma \)-convexity assumption. Further, a Mond–Weir type dual has been considered and weak and strong duality relations have been developed. Moreover, an application in robot trajectory planning has been considered and solved using MATLAB. In addition, considering the same trajectory as in Vaz et al. (Eur J Oper Res 153(3):607–617, 2004), we have compared the results obtained in MATLAB with the results available in Vaz et al. (Eur J Oper Res 153(3):607–617, 2004) and Haaren-Retagne (A semi-infinite programming algorithm for robot trajectory planning, 1992), where the authors have solved using AMPL. It has been observed that our results are more efficient than the previously available results, with the implementation of MATLAB as it substantially reduces the computational time. Throughout the paper, nontrivial examples have also been provided for proper justification of the theorems developed.