Characterizations and Applications of Prequasi-Invex Functions

X. M. Yang, X. Q. Yang and K. L. Teo

Journal of Optimization Theory and Applications, 2001, vol. 110, issue 3, No 9, 645-668

Abstract: Abstract In this paper, two new types of generalized convex functions are introduced. They are called strictly prequasi-invex functions and semistrictly prequasi-invex functions. Note that prequasi-invexity does not imply semistrict prequasi-invexity. The characterization of prequasi-invex functions is established under the condition of lower semicontinuity, upper semicontinuity, and semistrict prequasi-invexity, respectively. Furthermore, the characterization of semistrictly prequasi-invex functions is also obtained under the condition of prequasi-invexity and lower semicontinuity, respectively. A similar result is also obtained for strictly prequasi-invex functions. It is worth noting that these characterizations reveal various interesting relationships among prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions. Finally, prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions are used in the study of optimization problems.

Keywords: Prequasi-invex functions; strictly prequasi-invex functions; semistrictly prequasi-invex functions; semicontinuity; optimization (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017544513305

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