Resumen de Minimal approximate Hessians for continuously Gateaux differentiable functions

H. Li, F. Huang

• In this paper, we investigate minimal (weak) approximate Hessians, and completely answer the open questions raised by V. Jeyakumar and X. Q. Yang. As applications, we first give a generalised Taylor's expansion in terms of a minimal weak approximate Hessian. Then we characterise the convexity of a continuously Gateaux differentiable function. Finally some necessary and sufficient optimality conditions are presented.