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Efficiency conditions and duality for a class of multiobjective fractional programming problems. (English) Zbl 1106.90066
The authors study the multiobjective fractional programming problem (MFP): $\text{Min}\Biggl({f_i(x)\over g_1(x)}, {f_2(x)\over g_2(x)},\dots, {f_p(x)\over g_p(x)}\Biggr)$ s.t. $$h(x)\leq 0$$, $$x\in X$$, where $$X\subset \mathbb{R}^n$$ is an open set, $$f_i$$, $$g_i$$ $$(i= 1,2,\dots, p)$$ and $$h: X\to\mathbb{R}^m$$ are continuously differentiable functions on $$X$$. It is assumed that $$f_i(x)\geq 0$$ and $$g_i(x)> 0$$ for $$x\in X$$ and $$i= 1,2,\dots, p$$. The efficiency conditions and duality for MEP involving $$(F,\alpha,\rho, d)$$-convexity proposed by Z. A. Liang, H. X. Huang and P. M. Pardalos [J. Optim. Theory Appl. 110, No. 3, 611–619 (2001; Zbl 1064.90047)] are presented here.
Reviewer: R. N. Kaul (Delhi)

##### MSC:
 90C29 Multi-objective and goal programming 90C32 Fractional programming
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