On Characterizing the Solution Sets of Pseudoinvex Extremum Problems

X. M. Yang ()
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X. M. Yang: Chongqing Normal University

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 3, No 10, 537-542

Abstract: Abstract In this paper, we study the minimization of a pseudoinvex function over an invex subset and provide several new and simple characterizations of the solution set of pseudoinvex extremum problems. By means of the basic properties of pseudoinvex functions, the solution set of a pseudoinvex program is characterized, for instance, by the equality $\nabla f(x)^{T}\eta(\bar{x},x)=0$ , for each feasible point x, where $\bar{x}$ is in the solution set. Our study improves naturally and extends some previously known results in Mangasarian (Oper. Res. Lett. 7: 21–26, 1988) and Jeyakumar and Yang (J. Opt. Theory Appl. 87: 747–755, 1995).

Keywords: Pseudoinvex extremum problems; Solution sets; Characterizations; Invariant pseudomonotone maps (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-008-9470-7

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