Second-order and related extremality conditions in nonlinear programming

This paper is concerned with the problem of characterizing a local minimum of a mathematical programming problem with equality and inequality constraints. The main object is to derive second-order conditions, involving the Hessians of the functions, or related results where some other curvature information is used. The necessary conditions are of the Fritz John type and do not require a constraint qualification. Both the necessary conditions and the sufficient conditions are given in equivalent pairs of primal and dual formulations.This research was partly supported by Project No. NR-947-021, ONR Contract No. N00014-75-0569, with the Center for Cybernetic Studies, and by the National Science Foundation, Grant No. NSF-ENG-76-10260.