Abstract
In this paper, first-order optimality conditions for certain type of multi-objective optimisation problems are discussed under univexity concept. A number of duality results corresponding to this sort of multi-objective problems are also shown.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aghezzaf, B., & Hachimi, M. (2000). Generalised invexity and duality in multiobjective programming problems. Journal of Global Optimization, 18, 91–101.
Ehrgott, M. (2000). Multicriteria optimisation. Lecture notes in economics and mathematical systems. Berlin: Springer.
Ginchev, I., & Ivanov, V. I. (2008). Second-order optimality conditions for problems with C1 data. Journal of Mathematical Analysis and Applications, 340, 646–657.
Jeyakumar, V., & Mond, B. (1992). On generalised convex mathematical programming. Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 34, 43–53.
Maeda, T. (1994). Constraint qualification in multiobjective optimisation problems: Differentiable case. Journal of Optimization Theory and Applications, 80, 483–500.
Miettinen, K. (1999). Nonlinear multi-objective optimisation. Boston: Kluwer Academic.
Mishra, S. K. (1996). Generalised proper efficiency and duality for a class of nondifferentiable multiobjective variational problems with V-invexity. Journal of Mathematical Analysis and Applications, 202, 53–71.
Mishra, S. K. (1998). On multiple-objective optimisation with generalised univexity. Journal of Mathematical Analysis and Applications, 224, 131–148.
Mishra, S. K. (2000). Multiobjective second order symmetric duality with cone constraints. European Journal of Operational Research, 126, 675–682.
Mishra, S. K., & Giorgi, G. (2000). Optimality and duality with generalised semi-univexity. Opsearch, 37, 340–350.
Mishra, S. K., & Giorgi, G. (2008). Invexity and optimisation. Nonconvex optimisation and its applications (Vol. 88). Berlin: Springer.
Mishra, S. K., & Rueda, N. G. (2000). Higher-order generalised invexity and duality in mathematical programming. Journal of Mathematical Analysis and Applications, 247, 173–182.
Mishra, S. K., & Rueda, N. G. (2002). Higher-order generalised invexity and duality in nondifferentiable mathematical programming. Journal of Mathematical Analysis and Applications, 272, 496–506.
Mishra, S. K., Wang, S. Y., & Lai, K. K. (2005). Optimality and duality for multi-objective optimisation under generalised type I univexity. Journal of Mathematical Analysis and Applications, 303, 315–326.
Mishra, S. K., Wang, S. Y., & Lai, K. K. (2008). V-invex functions and vector optimisation. Optimisation and its applications (Vol. 14). New York: Springer.
Mishra, S. K., Wang, S. Y., & Lai, K. K. (2009). Generalised convexity and vector optimisation. Nonconvex optimisation and its applications (Vol. 90). Berlin: Springer.
Rizvi, M. M., & Nasser, M. (2006). New second-order optimality conditions in multiobjective optimisation problems: Differentiable case. Journal of the Indian Institute of Science, 86, 279–286.
Rueda, N. G., Hanson, M. A., & Singh, C. (1995). Optimality and duality with generalised convexity. Journal of Optimization Theory and Applications, 86, 491–500.
Sawaragi, Y., Nakayama, H., & Tanino, T. (1985). Theory of multi-objective optimisation. London: Academic Press.
Zhian, L., & Qingkai, Ye. (2001). Duality for a class of multiobjective control problems with generalised invexity. Journal of Mathematical Analysis and Applications, 256, 446–461.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Askar, S.S., Tiwari, A. First-order optimality conditions and duality results for multi-objective optimisation problems. Ann Oper Res 172, 277–289 (2009). https://doi.org/10.1007/s10479-009-0607-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-009-0607-3