Characterizations of pseudolinear and semistrictly quasilinear functions
DOI:
https://doi.org/10.24193/subbmath.2026.2.02Abstract
In this paper, we obtain several new complete characterizations of pseudolinear functions. Two of the results are of first-order and one is derivative free. The results are derived in terms of the Clarke-Rockafellar subdifferential. Additionally, we prove a characterization of the semistrictly quasilinear functions. It is similar to the derivative free characterization of the pseudolinear functions. We also find the conditions such that a semistrictly quasilinear function become pseudolinear.
References
[1] Ansari, Q. H., Schaible, S., Yao, J. C., η-pseudolinearity, Riviste di Matematice per le Scienze Economiche e Sociali, 22(1999), 31–39.
[2] Bazaraa, M. S., Shetty, C. M., Nonlinear Programming - Theory and Algorithms, John Wiley & Sons, New York, 1979.
[3] Bector, C. R., Singh, C., B-vex functions, J. Optim. Theory Appl., 71(1991), no. 2, 237–253.
[4] Bianchi, M., Hadjisavvas, N., Shaible, S., On pseudomonotone maps T for which −T is also pseudomonotone, J. Convex Anal. 10(2003), no. 1, 149–168.
[5] Cambini, A., Martein, L., Generalized Convexity and Optimization, Lecture Notes in Econom. and Math. Systems, Springer, Berlin, 616(2009).
[6] Chew, K. L., Choo, E. U., Pseudolinearity and efficiency, Math. Program. 28(1984), 226–239.
[7] Clarke, F. H., Optimization and nonsmooth analysis, A Wiley-Interscience Publication, John Wiley & Sons, New York, 1983.
[8] Daniilidis, A., Hadjisavvas, N., On the subdifferentials of quasiconvex and pseudoconvex functions and cyclic monotonicity, J. Math. Anal. Appl., 237(1999), 30–42.
[9] Giorgi, G., Guerraggio, A., Thierfelder, J., Mathematics of Optimization, Elsevier, Amsterdam, 2004.
[10] Ivanov, V. I., Characterizations of pseudoconvex functions and semistrictly quasiconvex ones, J. Glob. Optim., 57(2013), 677–693.
[11] Karamardian, S., Strictly quasi-convex (concave) functions and duality in mathematical programming, J. Math. Anal. Appl., 20(1967), 344–358.
[12] Karamardian, S., Complementarity over cones with monotone and pseudomonotone maps, J. Optim. Theory Appl., 18(1976), 445–454.
[13] Karamardian, S., Schaible, S., Seven kinds of monotone maps, J. Optim. Theory Appl. 66(1990), no. 1, 37–46.
[14] Komlósi, S., First and second order characterizations of pseudolinear functions, European J. Oper. Res. 67(1993), 278–286.
[15] Kortanek, K. O., Evans, J. P., Pseudoconcave programming and Lagrange regularity, Oper. Res 15(1967), 882–892.
[16] Lalitha, C. S., Mehta, M., A note of pseudolinearity in terms of bifunctions, Asia Pacific J. Oper. Res. 24(2007), 83–91.
[17] Lu, Q. H., Zhu, D. L., Some characterizations of locally Lipschitz pseudolinear functions, Math. Appl., 18(2005), 272–278.
[18] Mangasarian, O. L., Nonlinear Programming, Mc Graw-Hill, New York, 1969.
[19] Martos, B., Nonlinear Programming Theory and Methods, Akademiai Kiado, Budapest, 1975.
[20] Mishra, S. K., Upadhyay, B. B., Pseudolinear Functions and Optimization, Chapman & Hall Book, Boca Raton, 2015.
[21] Rapcsák, T., On pseudolinear functions, European J. Oper. Res. 50(1991), 353–360.
[22] Rezaci, M., Gazor, H., Nonsmooth pseudolinearity, Journal of Mathematical Extensions, 6(2012), no. 4, 63–77.
[23] Rockafellar, R. T., Generalized directional derivatives and subgradients of nonconvex functions, Canad. J. Math., 32(1980), 257–280.
[24] Schaible, S., Bibliography in fractional programming, Zeitschrift für Operations Research, 26(1982), no. 1, 211-241.
[25] Schaible, S., Ibaraki, T., Fractional programming, European J. Oper. Res, 12(1983), no. 4, 325–338.
[26] Stancu-Minasian, I. M., Fractional Programming. Theory, Methods, Applications, Mathematics and Its Applications, Springer, Berlin, 409(1997).
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