Second order duality for nondifferentiable multiobjective programming problem involving \((F, \alpha , \rho , d)-V\)-type I functions
The authors define classes of second-order (semi-strictly) \((F, \alpha,\rho,d)\)-V-type I and second-order (strictly) pseudoquasi \((F,\tilde \alpha,\tilde \rho,d)\)-V-type I functions. They study the multiobjective program \[ \min (f_i(x)+ (x^TB_ix)^{\frac{1}{2}}, i=1, \ldots, k) \] subject to \(x \in X =\{x: g(x) \leqq 0\}\), where \(f_i(x)\) are twice differentiable on \(X\) and \(B_i\) are \(n\times n\) positive semidefinite matrices. For both Mangasarian type and Mond-Weir type duals of this problem they prove weak, strong, and strict converse duality results.
scientific article; zbMATH DE number 5703324
scientific article