A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions

summary:A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order $\eta $-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order $\eta $-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order $\eta $-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem