Wyniki wyszukiwania - BazTech

1

Nonessential objective functions in linear multiobjective optimization problems

Malinowska A. B.

Control and Cybernetics

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2006

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Vol. 35, no 4

873-880

EN

In multiobjective (vector) optimization problems, among the given objective functions there exist some, which do not influence the set of efficient solutions. These objective functions are said to be nonessential. In this paper we present a new method to decide if a given linear objective function is nonessential or not.

2

Changes of the set of efficient solutions by extending the number of objectives and its evaluation

Malinowska A.

Control and Cybernetics

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2002

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Vol. 31, no 4

965-974

EN

In this paper the vector optimization problem P with continuous and convex objective functions on a compact convex feasible set is considered. We form a new vector optimisation problem P* from P by adding an objective function to the problem P. The necessary and sufficient conditions for the sets of efficient solutions of these two problems to be equal are given. In the case where the set of efficient solutions of the problem P* contains that of P, we also suggest how the difference between the sets of efficient solutions of the problems P* and P might be evaluated. Examples are given to illustrate our results.

PL

W artykule rozważa się zadanie optymalizacji wektorowej P z ciągłymi i wypukłymi funkcjami celu na zwartym wypukłym zbiorze rozwiazań dopuszczalnych. Tworzymy nowe zadanie optymalizacji wektorowej P* poprzez dodanie funkcji celu do zadania P. Podano warunki konieczne i wystarczające do tego, by zbiory rozwiązań sprawnych obu zadań były równe. Dla przypadku, gdy zbiór rozwiązan sprawnych zadania P* zawiera odpowiedni zbiór dla P, zaproponowano także sposób oceny różnicy między tymi zbiorami rozwiązań sprawnych. Wyniki podane w artykule zostały zilustrowane przykładami.

3

Multiobjective programming with (p, r)-invexity

Antczak T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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2001

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z. 25 [190]

31-46

EN

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.

4

Second-order necessary conditions of the Kuhn-Tucker type in multiobjective programming problems

Aghezzaf B.

Control and Cybernetics

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1999

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Vol. 28, no 2

213-224

EN

In this paper, we are concerned with a multiobjective programming problem with inequality constraints. We develop second-order necessary condition of the Kuhn-Tucker type for effciency and prove that the condition holds under a. constraint qualification. Moreover, we give some conditions which ensure that the constraint qua,lifica.tion holds.