Continuous-time optimization problems involving invex functions

In [D.H. Martin, The essence of invexity, J. Optim. Theory Appl. 47 (1985) 65–76] Martin introduced the notions of KKT-invexity and WD-invexity for mathematical programming problems. These notions are relaxations of invexity. In this work we generalize these concepts for continuous-time nonlinear optimization problems. We prove that the notion of KKT-invexity is a necessary and sufficient condition for global optimality of a Karush–Kuhn–Tucker point and that the notion of WD-invexity is a necessary and sufficient condition for weak duality.