Duality for multiple objective fractional programming with generalized type-I univexity. (English) Zbl 1375.90289

Stancu-Minasian, Ioan M.; Stancu, Andreea Mădălina

Migdalas, Athanasios (ed.) et al., Optimization theory, decision making, and operations research applications. Proceedings of the 1st international symposium and 10th Balkan conference on operational research, Thessaloniki, Greece, September 22–25, 2011. New York, NY: Springer (ISBN 978-1-4614-5133-4/hbk; 978-1-4614-5134-1/ebook). Springer Proceedings in Mathematics & Statistics 31, 199-209 (2013).

Summary: In this paper, a multiobjective fractional subset programming problem (Problem (P)) is considered. A new class of \((\mathcal{F},b,\phi,\rho,\theta)\)-type-I univex function is introduced and a general dual model for (P) is presented. Based on these functions, weak, strong and converse duality theorems are derived. Almost all results presented in the literature were obtained under the assumption that the function \(\mathcal{F}\) is sublinear in the third argument. Here, our results hold assuming only the convexity of this one.
For the entire collection see [Zbl 1255.90010].

MSC:

90C32	Fractional programming
90C29	Multi-objective and goal programming
90C46	Optimality conditions and duality in mathematical programming