A new two-level linear relaxed bound method for geometric programming problems

In this paper a new two-level linear relaxed bound method is proposed for solving the global solution of geometric programming problems, and its convergent properties is proved, and a numerical example is used to illustrate the effectiveness of the presented algorithm. The bound technique in this algorithm is different from the other ones. The two-level relaxed linear programming problems of geometric programming problems are given without additional new variables and constraints by making use of the linear approximation of power functions and the new formulas for product to be unequal with sum.

[1]  Harold P. Benson,et al.  Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic , 1997 .

[2]  Hiroshi Konno,et al.  BOND PORTFOLIO OPTIMIZATION BY BILINEAR FRACTIONAL PROGRAMMING , 1989 .

[3]  Ignacio E. Grossmann,et al.  A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms , 1999, J. Glob. Optim..

[4]  James E. Falk,et al.  Jointly Constrained Biconvex Programming , 1983, Math. Oper. Res..

[5]  Pierre Hansen,et al.  Reduction of indefinite quadratic programs to bilinear programs , 1992, J. Glob. Optim..

[6]  Siegfried Schaible,et al.  Finite algorithm for generalized linear multiplicative programming , 1995 .

[7]  F. Cole,et al.  A comparison between a primal and a dual cutting plane algorithm for posynomial geometric programming problems , 1985 .

[8]  Brigitte Jaumard,et al.  Generalized Convex Multiplicative Programming via Quasiconcave Minimization , 1995, J. Glob. Optim..

[9]  Hiroshi Konno,et al.  An outer approximation method for minimizing the product of several convex functions on a convex set , 1993, J. Glob. Optim..

[10]  Harold P. Benson,et al.  An Outcome Space Branch and Bound-Outer Approximation Algorithm for Convex Multiplicative Programming , 1999, J. Glob. Optim..

[11]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

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

[13]  Hanif D. Sherali,et al.  A new reformulation-linearization technique for bilinear programming problems , 1992, J. Glob. Optim..

[14]  Yves Smeers,et al.  Reversed geometric programming: A branch-and-bound method involving linear subproblems , 1980 .

[15]  Hiroshi Konno,et al.  Generalized linear multiplicative and fractional programming , 1991 .

[16]  C. Floudas,et al.  A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—I. Theory , 1990 .

[17]  N. Sahinidis,et al.  Global optimization of nonconvex NLPs and MINLPs with applications in process design , 1995 .

[18]  Pierre Hansen,et al.  Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions , 1992, J. Glob. Optim..

[19]  Hanif D. Sherali,et al.  A reformulation-convexification approach for solving nonconvex quadratic programming problems , 1995, J. Glob. Optim..

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

[21]  Hanif D. Sherali,et al.  Comparison of Two Reformulation-Linearization Technique Based Linear Programming Relaxations for Polynomial Programming Problems , 1997, J. Glob. Optim..