A Global Optimization Method for Nonlinear Fractional Programs

一個處理非線性分式規劃的全域最佳化方法

余強生(Chian-Son Yu) ； 黎漢林(Han-Lin Li)

《Pan-Pacific Management Review》 6卷2期 (2003/07) Pp. 159-178

https://doi.org/10.30166/PPMR.200307.0003

摘要

雖然全域最佳化的研究，在二十世紀之末已經顯著的有所增加，但針對分式規劃所作的全域最佳化研究仍然顯得很少，特別肇因於非線性分式規劃的複雜度，因此有關非線性分式規劃全域最佳化的研究就更稀少了。不過在現實的管理活動中，卻經常地有非線性分式規劃的指標須要處理，例如：財務規劃的比值（負債／資產）、生產計劃的比值（產出／投入員工數）等。雖然有鑑於線性分式規劃較易於計算，因此線性分式規劃常被用來處理許多含有分式規劃指標的決策問題，但在實務上，非線性分式規劃卻顯著地要比線性規劃更能表現出真實決策問題的現況。也因此，本研究的目的就在於：提出一個全域最佳化方法來求解非線性分式規劃的問題。

關鍵字

分式規劃 ； 最佳化 ； 非線性函數

並列摘要

Despite extensive research has been undertaken on global optimization during the late 20(superscript th) century, global optimization methods have not often been applied to fractional programming, especially for nonlinear fractional programs owing to its complexity. Since management activities frequently desire to optimize certain indicators in various proportions, such as financial planning (debt/equity ratio), production planning (output/employee ratio), etc., many decisional models have been considered as fractional programs. Accordingly, linear fractional programming has been widely applied in numerous management problems due to its simplicity. However, linear fractional programming cannot describe all real-life problems, and unfortunately a nonlinear fractional program describes most practical problems significantly better than a linear fractional program does. Therefore, this study aims to develop a global optimization method for solving nonlinear fractional programming problems.

並列關鍵字

Fractional Programming ； Optimization ； Nonlinear Function

參考文獻

Bector, C. R.,Bhatt, S. K.(1978).Pseudo-Monotonic Interval Programming.Naval Research Logistic Quart.25(2),309-314.

Bector, C. R.,Chandra, S.,Gulati, T. R.(1973).Duality for Complex Nonlinear Fractional Programming Over Cones.Proceedings of the Third Manitoba Conference on Numerical Mathematics.(Proceedings of the Third Manitoba Conference on Numerical Mathematics).

Bhatt, S. K.(1989).Equivalence of Various Linearization Algorithms for Linear Fractional Programming.Operations Research.33(1),39-43.

Bernard, J. C.,Ferland, J. A.(1989).Convergence of Interval-Type Algorithms for Generalized Fractional Programming.Mathematical Programming.43,349-364.

Borde, J.,Crouzeix, J. P.(1987).Convergence of a Dinkelbach-Type Algorithm in Generalized Fractional Programming.Zeitschrift fur Operations Research.31,31-54.