Second-order optimality conditions for \(C^1\) multiobjective programming problems (Q696130)

There exist a huge number of papers in which continuously differentiable problems with inequality constraints are stuidied. Quite few publications exist on second order conditions. The purpose if the paper is to establish such conditions for constrained multiobjective programming problems with continuously differentiable data (named \(C^1\) data). In the paper the definition of approximate Jacobian and approximate Hessian is recalled (section 2). Then necessary conditions (section 3) and sufficient conditions (section 4) are formulated and proved. In the example (section 5) it is shown how the recession Hessian matrices cannot be removed when the data of the problem are of class \(C^1\).