Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 30 Issue 1
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- Pages.1-7
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- 1993
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
GENERALIZATIONS OF ISERMANN'S RESULTS IN VECTOR OPTIMIZATION
Abstract
Vector optimization problems consist of two or more objective functions and constraints. Optimization entails obtaining efficient solutions. Geoffrion [3] introduced the definition of the properly efficient solution in order to eliminate efficient solutions causing unbounded trade-offs between objective functions. In 1974, Isermann [7] obtained a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with linear constraints and showed that every efficient solution is a properly efficient solution. Since then, many authors [1, 2, 4, 5, 6] have extended the Isermann's results. In particular, Gulati and Islam [4] derived a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with nonlinear constraints, under certain assumptions. In this paper, we consider the following nonlinear vector optimization problem (NVOP): (Fig.) where for each i, f
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