After a brief survey of the literature about sufficient conditions, we give
different sufficient conditions of optimality for infinite-horizon calculus
of variations problems in the general (non concave) case. Some sufficient
conditions are obtained by extending to the infinite-horizon setting the
techniques of extremal fields. Others are obtained in a special
qcase of reduction to finite horizon. The last result uses auxiliary
functions. We treat five notions of optimality. Our problems are essentially
motivated by macroeconomic optimal growth models.