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Multiobjective duality with invexity. (English) Zbl 0635.90086

The concept of proper efficiency as first defined by Geoffrion is used to construct duality relations between two multiobjective differentiable nonlinear programming problems. Appropriate positive linear combinations of the functions are required to be invex over an appropriate feasible region. Weak duality requires only the invexity of positive linear combinations of the functions. Strong duality results require a constraint qualification, proper efficiency as well as invexity.
Strong duality results are established via a parametric programming problem obtained from the primal using a fixed positive weight vector. A kind of converse duality parallelling strict converse duality in single objective nonlinear programming is also given.
Reviewer: R.R.Egudo

MSC:

90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming
49N15 Duality theory (optimization)
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