Comparison of Two Reformulation-Linearization Technique Based Linear Programming Relaxations for Polynomial Programming Problems

In this paper, we compare two strategies for constructing linear programmingrelaxations for polynomial programming problems using aReformulation-Linearization Technique (RLT). RLT involves an automaticreformulation of the problem via the addition of certain nonlinear impliedconstraints that are generated by using the products of the simple boundingrestrictions (among other products), and a subsequent linearization based onvariable redefinitions. We prove that applying RLT directly to the originalpolynomial program produces a bound that dominates in the sense of being atleast as tight as the value obtained when RLT is applied to the jointcollection of all equivalent quadratic problems that could be constructed byrecursively defining additional variables as suggested by Shor.

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

[2]  Christodoulos A. Floudas,et al.  Unconstrained and constrained global optimization of polynomial functions in one variable , 1992, J. Glob. Optim..

[3]  Ignacio E. Grossmann,et al.  A global optimization algorithm for linear fractional and bilinear programs , 1995, J. Glob. Optim..

[4]  C. Floudas,et al.  Primal-relaxed dual global optimization approach , 1993 .

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

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

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

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

[9]  FAIZ A. AL-KHAYYAL,et al.  A relaxation method for nonconvex quadratically constrained quadratic programs , 1995, J. Glob. Optim..

[10]  Pierre Hansen,et al.  An analytical approach to global optimization , 1991, Math. Program..

[11]  N. Shor.  Dual quadratic estimates in polynomial and Boolean programming , 1991 .

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

[13]  K. Grasse,et al.  A general class of branch-and-bound methods in global optimization with some new approaches for concave minimization , 1986 .