New Second-Order Optimality Conditions in Multiobjective Optimization Problems: Differentiable Case

To get positive Lagrange multipliers associated with each of the objective function, Maeda [Constraint qualification in multiobjective optimization problems: Differentiable case, J. Optimization Theory Appl., 80, 483-500 (1994)], gave some special sets and derived some generalized regularity conditions for first-order Karush-Kuhn-Tucker (KKT)-type necessary conditions of multiobjective optimization problems. Basing on Maeda's set, Bigi and Castellani [Second order optimality conditions for differentiable multiobjective problems, RAIRO, Op. Res., 34, 411-426 (2000)], tried to get the same result for second-order optimality conditions but their treatment was not convincing. In this paper, we have generalized these regularity conditions for second-order optimality conditions under different sets and obtained positive Lagrange multipliers for the objective function.