In the present paper, we are concerned with a minimax fractional programming problem containing arbitrary norms and establish duality theorems for a dual model related to minimax fractional programming problem under the assumptions of second order (Φ, ρ)-invexity.

In this note we study multiple-ratio fractional 0–1 programs, a broad class of $$\mathcal {NP}$$ -hard combinatorial optimization problems. particular, under some relatively mild assumptions provide complete characterization the conditions, which ensure that single-ratio function is submodular. Then illustrate our theoretical results with assortment and facility location problems, discuss pract...

‎in this paper, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. we consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. within this context, define generalized mangasarian-fromovitz constraint qualification and show t...