Generalized Continuous Nondifferentiable Fractional Programming Problems with Invexity

Abstract

The concept of invexity has allowed the convexity requirements in a variety of mathematical programming problems to be weakened. We extend a number of Kuhn-Tucker type sufficient optimality criteria for a class of continuous nondifferentiable minmax fractional programming problems that involves several ratios in the objective with a nondifferentiable term in the numerators. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalized invexity assumptions. These results extend many well-known duality results and also give a dynamic generalization of those of finite dimensional nonlinear programming problems recently explored.