Applications to Continuous Problems

Abstract

In Part II of this book, we have presented a Reformulation-Linearization/Convexification Technique for generating tight polyhedral or convex relaxations for polynomial programming problems. We have shown how the lower bounds generated by this technique can be embedded within a branch-and-bound algorithm and used in concert with a suitable partitioning procedure in order to induce infinite convergence, in general, to a global optimum for the underlying nonconvex polynomial program. In some special cases, as we shall see in this chapter, finite convergence can be obtained by exploiting inherent problem structures and characteristics. In Chapters 8 and 9, we have also presented some particular RLT strategies for generating tight relaxations for quadratic as well as for general polynomial programs and have illustrated the computational strength of the proposed procedures. In the present chapter, we complement this discussion by describing the design of RLT-based algorithms for some other special applications. The purpose of this exposition is to exhibit by way of illustration how RLT can be used for constructing such algorithms for a variety of nonconvex programming problems.