Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 23 Issue 2
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- Pages.141-148
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- 1986
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
A PSEUDOCONVEX PROGRAMMINA IN A HILBERT SPACE
Abstract
In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.
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