THE l1 EXACT EXPONENTIAL PENALTY FUNCTION METHOD WITH (p, r) − ρ − (η, θ)-INVEXITY

In this paper, the l1 exact exponential penalty function method is used to solve the nonlinear mathematical programming problems with (p, r) − ρ − (η, θ)-invex functions. We characterize the solutions of the constrained optimization problem in terms of solutions of the corresponding unconstrained problem. The equivalence between sets of optimal solutions of the original mathematical programming problem and its associated exponential penalized optimization problem is established under suitable (p, r) − ρ − (η, θ)-invexity assumptions. As an application we solve the optimal control problem by considering the corresponding unconstrained reformulation with the l1 exact exponential penalty function method. Examples and some counter examples are also illustrated.