Second-order optimality conditions for nonlinear programs and mathematical programs

It is well known that second-order information is a basic tool notably in optimality conditions and numerical algorithms. In this work, we present a generalization of optimality conditions to strongly convex functions of order gamma with the help of firstand second-order approximations derived from (Optimization 40(3): 229-246, 2011) and we study their characterization. Further, we give an example of such a function that arises quite naturally in nonlinear analysis and optimization. An extension of Newton's method is also given and proved to solve Euler equation with second-order approximation data.