On the posynomial fractional programming problems

Abstract The posynomial fractional programming (PFP) problem arises from the summation minimization of several quotient terms, which are composed of posynomial terms appearing in the objective function subject to given posynomial constraints. This paper proposes an approximate approach to solving a PFP problem. A linear programming relaxation is derived for the problem based on piecewise linearization techniques, which first convert a posynomial term into the sum of absolute terms; these absolute terms are then linearized by some linearization techniques. The proposed approach could reach a solution as close as possible to a global optimum.

[1]  P. Robillard.  (0, 1) hyperbolic programming problems , 1971 .

[2]  Abraham Charnes,et al.  Programming with linear fractional functionals , 1962 .

[3]  Han-Lin Li.  A GLOBAL APPROACH FOR GENERAL 0-1 FRACTIONAL-PROGRAMMING , 1994 .

[4]  Ching-Ter Chang,et al.  On the polynomial mixed 0-1 fractional programming problems , 2001, Eur. J. Oper. Res..

[5]  M. Gugat.  A Fast Algorithm for a Class of Generalized Fractional Programs , 1996 .

[6]  Tai-Hsi Wu.  A note on a global approach for general 0-1 fractional programming , 1997 .

[7]  Jacques A. Ferland,et al.  Algorithms for generalized fractional programming , 1991, Math. Program..

[8]  Hanif D. Sherali,et al.  A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique , 1992, J. Glob. Optim..

[9]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[10]  Hartmut Wolf,et al.  A Parametric Method for Solving the Linear Fractional Programming Problem , 1985, Oper. Res..

[11]  C Tofallis,et al.  Fractional Programming: Theory, Methods and Applications , 1997, J. Oper. Res. Soc..

[12]  Hanif D. Sherali,et al.  Global Optimization of Nonconvex Polynomial Programming Problems Having Rational Exponents , 1998, J. Glob. Optim..

[13]  Dimitris K. Despotis,et al.  Fractional Minmax Goal Programming: A Unified Approach to Priority Estimation and Preference Analysis in MCDM , 1996 .

[14]  I. M. Stancu-Minasian,et al.  A sixth bibliography of fractional programming , 2006 .

[15]  Y. Anzai.  ON INTEGER FRACTIONAL PROGRAMMING , 1974 .

[16]  Han-Lin Li,et al.  An approximate approach of global optimization for polynomial programming problems , 1998, Eur. J. Oper. Res..

[17]  Mordecai Avriel,et al.  Complementary Geometric Programming , 1970 .

[18]  Ching-Ter Chang,et al.  An efficient linearization approach for mixed-integer problems , 2000, Eur. J. Oper. Res..

[19]  Han-Lin Li,et al.  A global optimization method for nonconvex separable programming problems , 1999, Eur. J. Oper. Res..