Précis--Sufficiency Conditions for Constrained Optima

The sufficiency conditions for constrained optimization problems are derived through an alternate approach and result in a simpler form than one latest work [Schechter, R. S., G. S. G. Beveridge. 1966. Sufficiency conditions in constrained variations. Indus. Eng. Chemistry Fundamentals 5 571-573.]. The relations can be used with equality and/or inequality constraints. The sufficiency conditions of Phipps [Phipps, C. G. 1952. Maxima and minima under restraint. Amer. Math. Monthly 59 230-235.] which have been quoted for years in the literature were corrected in this work.