Second-order sufficient conditions for infinite-dimensional extremal problems

In this paper the author studies the following constrained mathematical programming problem: minleft{f_0(x)colon F(x)=0, f_i(x)leq 0, i=1,dots,kright}, where Fcolon Xto Y, f_icolon Xto Bbb R (i=0,1,dots,k), X and Y are normed spaces. Under second-order differentiability assumptions imposed upon the objective and the constraints, a second-order sufficient condition for optimality is established. Some discussions about this result together with some illustrative examples are also given.