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Multiobjective programming with (p, r)-invexity

Antczak T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2001

z. 25 [190]

31-46

A nonlinear multiobjective programming problem is considered where the functions involved are differentiable. In this work, we generalize some scalar optimization theory results making them applicable to vectorial optimization. By using the concept of (p, r)-invexity we give a new characterization of solutions of multiobjective programming problems. To do this, we introduce the definitions of stationary points and Kuhn-Tucker points for multiobjective programming problems. We prove, for unconstrained multiobjective programming problems with (p,r)-invex functions, that the equivalence between optimal solutions and stationary points remains true when several objective functions are optimized instead of one objective function. Moreover, we give two types of Kuhn-Tucker optimality conditions for constrained multiobjective programming problems. For this purpose, we generalize Martin's [16] definition of KT-invex problems to vectorial optimization problems with (p,r)-invex functions.

Fractional programming with (p,r)-invexity

Antczak T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2001

z. 25 [190]

5-29

The notion of (p, r)-invexity for a vector function is introduced and discussed its application to a class of fractional problems. Parametric and non-parametric necessary and sufficient optimality conditions and duality results for a generalized fractional programming are obtained under an appropriate (p,r)-invexity assumption on involving functions.