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On characterizations of prequasi-invex functions. (English) Zbl 1100.90035
Summary: In [J. Optim. Theory Appl. 110, No. 3, 645–668 (2001; Zbl 1064.90038)] X. M. Yang, X. Q. Yang and K. L. Teo presented characterizations of prequasi-invex functions, semistrictly prequasi-invex functions, and strictly prequasi-invex functions, respectively, under a certain set of conditions. In this note, we show that the same results or even more general ones can be obtained under weaker assumptions.

MSC:
90C26 Nonconvex programming, global optimization
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[1] Yang, X. M., Yang, X. Q., and Teo, K. L., Characterizations and Applications of Prequasi-Invex Functions, Journal of Optimization Theory and Applications, Vol. 110, No. 3, pp. 645-668, 2001. · Zbl 1064.90038 · doi:10.1023/A:1017544513305
[2] Mukherjee, R. M., and Reddy, L. V., Semicontinuity and Quasiconvex Functions, Journal of Optimization Theory and Applications, Vol. 94, No. 3, pp. 715-726, 1997. · Zbl 0892.90145 · doi:10.1023/A:1022609218907
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