Efficiency conditions and duality for a class of multiobjective fractional programming problems. (English) Zbl 1106.90066

Liang, Zhi-An; Huang, Hong-Xuan; Pardalos, Panos M.

J. Glob. Optim. 27, No. 4, 447-471 (2003).

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

Keywords:

multiobjective fractional programming problem; \((F,\alpha,\rho,d)\)-convex function; efficiency; duality