References
- Hanson MA. On sufficiency of the Kuhn-Tucker conditions. J Math Anal Appl. 1981;80(2):545–550. doi: 10.1016/0022-247X(81)90123-2
- Zalmai GJ. Generalized sufficiency criteria in continuous-time programming with application to a class of variational-type inequalities. J Math Anal Appl. 1990;153(2):331–355. doi: 10.1016/0022-247X(90)90217-4
- Yang XM, Li D. Semistrictly preinvex functions. J Math Anal Appl. 2001;258(1):287–308. doi: 10.1006/jmaa.2000.7382
- Rapcsak T. Geodesic convexity in nonlinear optimization. Optim Theory Appl. 1999;69(1):169–183. doi: 10.1007/BF00940467
- Udriste C. Convex functions and optimization methods on Riemannian manifolds. Vol. 297. Springer Science and Business Media Dordrecht; 2013.
- Pini R. Convexity along curves and invexity. Optimization. 1994;29(4):301–309. doi: 10.1080/02331939408843959
- Mititelu S. Generalized invexity and vector optimization on differentiable manifolds. Differ Geom Dyn Syst. 2001;3:21–31.
- Ferrara M, Mititelu S. Mond-Weir duality in vector programming with generalized invex functions on differentiable manifolds. Balkan J Geomet Appl. 2006;11(2):80–87.
- Jeyakumar V. Convexlike alternative theorems and mathematical programming. Optimization. 1985;16(5):643–652. doi: 10.1080/02331938508843061
- Singh A, Suneja SK, Rueda NG. Preinvexity in multiobjective fractional programming. J Inform Optim Sci. 1992;13(2):293–302.
- Caristi G, Ferrara M, Stefanescu A. Semi-infinite multiobjective programming with generalized invexity. Math Reports. 2010;62:217–233.
- Butt SI, Budak H, Tariq M, et al. Integral inequalities for n–polynomial s-type preinvex functions with applications. Math Methods Appl Sci. 2021;44(14):11006–11021. doi: 10.1002/mma.7465
- Noor MA, Noor KI. New classes of preinvex functions and variational-like inequalities. Filomat. 2021;35(6):2081–2097. doi: 10.2298/FIL2106081N
- Kiliçman A, Saleh W. Generalized preinvex functions and their applications. Symmetry. 2018;10(10):493. doi: 10.3390/sym10100493
- Ali M, Akhter E. X-convexity and applications of quasi-X-convex functions. arXiv preprint arXiv:2208.06589.2022.
- Ansari QH, Lalitha CS, Mehta M. Generalized convexity, nonsmooth variational inequalities, and nonsmooth optimization. CRC Press New York ; 2013.
- Asadi M. Hermite-Hadamard (HH) integral inequality for M, Q pre-invex function. Intell Multimed Process Commun Syst (IMPCS). 2023;4(1):11–6.
- Das K, Nahak C. Sufficiency and duality in set-valued optimization problems under (p,r)−ρ−(η,θ)-invexity. Acta Univ Apulensis. 2020;62:93–110.
- Dubey R, Mishra VN. New type of G-Mond-Weir type primal-dual model and their duality results with generalized assumptions. Filomat. 2021;35(9):2869–2882. doi: 10.2298/FIL2109869D
- Joshi BC. Mathematical programs with vanishing constraints involving strongly invex functions. Numer Algorithms. 2022; 91(2):505–530.
- Noor MA, Noor KI. Properties of higher order preinvex functions. Numer Algebra Control Optim. 2021;11(3):431. doi: 10.3934/naco.2020035
- Reddy LV, Singh A, Pandey SP. Generalized invexity and semi-continuity in mathematical programming. Int J Appl Eng Res. 2019;14(12):2960–2967.
- Sial IB, Ali MA, Murtaza G, et al. On some new inequalities of Hermite–Hadamard midpoint and trapezoid type for preinvex functions in p, q-Calculus. Symmetry. 2021;13(10):1864. doi: 10.3390/sym13101864
- Tariq M, Sahoo SK, Jarad F, et al. Some integral inequalities for generalized preinvex functions with applications. AIMS Math. 2021;6(12):13907–13930. doi: 10.3934/math.2021805
- Yang XM, Yang XQ, Teo KL. Characterizations and applications of prequasi-invex functions. J Optim Theory Appl. 2001;110(3):645–668. doi: 10.1023/A:1017544513305
- Za˘linescu C. A critical view on invexity. J Optim Theory Appl. 2014;162(3):695–704. doi: 10.1007/s10957-013-0506-2
- Weir T, Jeyakumar V. A class of nonconvex functions and mathematical programming. Bull Aust Math Soc. 1988;38(2):177–89. doi: 10.1017/S0004972700027441
- Weir T, Mond B. Preinvex functions in multiple objective optimization. J Math Anal Appl. 1988;136(1):29–38. doi: 10.1016/0022-247X(88)90113-8
- Pini R. Invexity and generalized convexity. Optimization. 1991;22(4):513–525. doi: 10.1080/02331939108843693