A Class of Nondifferentiable Fractional Programming Problems
B. Mond · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1978
Abstract Recently Chandra and Gulati established duality theorems for the nondifferentiable fractional programming problem maximize< [cTx – (xTBx)1/2 – α]/[eTx + (xTDx)1/2 + β] subject to Ax ≦ b, x≧. Here we treat the more general nonlinear fractional programming problem maximize [f(x) – (xT Bx)1/2]/[g(x) + (xT Dx)1/2] subject to h(x) ≦0, where f, g and h are differentiable, possibly nonlinear, functions. Necessary and sufficient conditions for optimality as well as appropriate duality theorems are established.