Duality for non-differentiable multi-objective semi-infinite programming for higher order invex functions (Q2204609)

Summary: This paper deals with non-differentiable multi-objective semi-infinite programming problem. It is a problem of simultaneous minimisation of finitely many scalar valued functions subject to an arbitrary (possibly infinite) set of constraints. Non-differentiability enters, due to the square root of a quadratic form which appears in the objective functional. Concept of efficiency of order \(m\) has been extended to the above stated problem. In order to study this new solution concept, the notion of \(\rho\)-invexity of order \(m\) is also proposed which is utilised to establish sufficient optimality conditions for the non-differentiable multi-objective semi-infinite programming problem. Mond-Weir type of dual is proposed for which weak, strong and strict converse duality theorems are established.