A DC Programming Approach to Fractional Problems

被引:0
作者
Gruzdeva, Tatiana [1 ]
Strekalovsky, Alexander [1 ]
机构
[1] SB RAS, Matrosov Inst Syst Dynam & Control Theory, Lermontov Str 134, Irkutsk 664033, Russia
来源
LEARNING AND INTELLIGENT OPTIMIZATION (LION 11 2017) | 2017年 / 10556卷
基金
俄罗斯科学基金会;
关键词
Fractional optimization; Nonconvex problem; Difference of two convex functions; Equation with vector parameter; Global search algorithm; SUM;
D O I
10.1007/978-3-319-69404-7_27
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper addresses a rather general fractional optimization problem. There are two ways to reduce the original problem. The first one is a solution of an equation with the optimal value of an auxiliary d.c. optimization problem with a vector parameter. The second one is to solve the second auxiliary problem with nonlinear inequality constraints. Both auxiliary problems turn out to be d.c. optimization problems, which allows to apply Global Optimization Theory [1 1 ,12] and develop two corresponding global search algorithms that have been tested on a number of test problems from the recent publications.
引用
收藏
页码:331 / 337
页数:7
相关论文
共 14 条
[1]   An effective algorithm for globally solving a class of linear fractional programming problem [J].
Ma, Baolin ;
Geng, Lei ;
Yin, Jingben ;
Fan, Liping .
Journal of Software, 2013, 8 (01) :118-125
[2]   Minimizing the sum of many rational functions [J].
Bugarin F. ;
Henrion D. ;
Lasserre J.B. .
Mathematical Programming Computation, 2016, 8 (01) :83-111
[3]  
Dinkelbach W., 1967, Manage. Sci., V13, P492
[4]   Solving the sum-of-ratios problem by an interior-point method [J].
Freund, RW ;
Jarre, F .
JOURNAL OF GLOBAL OPTIMIZATION, 2001, 19 (01) :83-102
[5]   An Approach to Fractional Programming via DC Optimization [J].
Gruzdeva, Tatiana ;
Strekalovskiy, Alexander .
NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA-2016), 2016, 1776
[6]   An Approach to Fractional Programming via DC Constraints Problem: Local Search [J].
Gruzdeva, Tatiana ;
Strekalovsky, Alexander .
DISCRETE OPTIMIZATION AND OPERATIONS RESEARCH, DOOR 2016, 2016, 9869 :404-417
[7]   A simplex algorithm for piecewise-linear fractional programming problems [J].
Pandey, Pooja ;
Punnen, Abraham P. .
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2007, 178 (02) :343-358
[8]  
Raouf O. A., 2014, J IND ENG INT, V10, P56
[9]   Fractional programming: The sum-of-ratios case [J].
Schaible, S ;
Shi, JM .
OPTIMIZATION METHODS & SOFTWARE, 2003, 18 (02) :219-229
[10]  
Strekalovsky A.S., 2014, Optimization in Science and Engineering, P465, DOI [10.1007/978-1-4939-0808-0_23, DOI 10.1007/978-1-4939-0808-0_23]