Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualifications

We are concerned with a nonlinear programming problem with equality and inequality constraints. We shall give second-order necessary conditions of the Kuhn-Tucker type and prove that the conditions hold under new constraint qualifications. The constraint qualifications are weaker than those given by Ben-Tal (Ref. 1).The author would like to thank Professor N. Furukawa and the referees for their many valuable comments and helpful suggestions.