Multiobjective Fractional Programming
Numerous decision problems in management science and problems in economic theory give rise to constrained optimization of linear or nonlinear functions. If in the nonlinear case the objective function is a ratio of two functions or involves several such ratios, then the optimization problem is called a fractional program.
Apart from isolated earlier results, most of the work in fractional programming were done since about 1960. The analysis of fractional programs with only one ratio has largely dominated the literature until about 1980. Since the first international conference with an emphasis on fractional programming the NATO advanced Study Institute on “Generalized Concavity in Optimization and Economics” (Schaible and Ziemba (1981)), that indicates a shift of interest from the single to the multiobjective case, see Singh and Dass (1989), Cambini, Castagnoli, Martein, Mazzoleni and Schaible (1990), Komlosi, Rapcsak and Schaible (1994), Mazzoleni (1992). It is interesting to note that some of the earliest publications in fractional programming, though not under this name, Von Neuman’s classical paper on a model fo a general economic equilibrium [Von Neumann (1937)] analysis a multiobjective fractional program. Even a duality theory was proposed for this nonconcave program, and this at a time when linear programming hardly existed. However, this early paper was followed almost exclusively by articles in single objective fractional programming until the early 1980s.
KeywordsEfficient Solution Constraint Qualification Strong Duality Fractional Programming Weak Duality
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