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Optimality conditions in multiobjective differentiable programming. (English) Zbl 0593.90071
Necessary conditions not requiring convexity are based on the convergence of a vector at a point and on Motzkin’s theorem of the alternative. A constraint qualification is also involved in the establishment of necessary conditions. Three theorems on sufficiency require various levels of convexity on the component of the functions involved, and the equality constraints are not necessarily linear. Scalarization of the objective function is used only in the last sufficiency theorem.

MSC:
90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
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