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This book presents with the thought and functions of the Reformulation- Linearization/Convexification Technique (RL T) for fixing nonconvex optimization points. A unified treatment of discrete and regular nonconvex programming points is launched using this technique. In essence, the bridge between these two sorts of nonconvexities is made by means of a polynomial illustration of discrete constraints. For example, the binariness on a zero-1 variable x . could also be equivalently J expressed as a result of the polynomial constraint x . (1-x . ) = zero. The motivation for this book is J J the place of tight linear/convex programming representations or relaxations in fixing such discrete and regular nonconvex programming points. The principal thrust is to start with a model that affords a useful illustration and development, and then to further strengthen this illustration by the use of automated reformulation and constraint period strategies. As talked about above, the focal degree of this book is the occasion and software of RL T for use as an automatic reformulation course of, and moreover, to generate strong professional inequalities. The RLT operates in two phases. Inside the Reformulation Half, positive sorts of additional implied polynomial constraints, that embrace the aforementioned constraints inside the case of binary variables, are appended to the difficulty. The following disadvantage is subsequently linearized, apart from that positive convex constraints are sometimes retained in XV particular specific situations, inside the Linearization/Convexijication Half. That’s achieved by means of the definition of applicable new variables to trade each distinct variable-product time interval. The higher dimensional illustration yields a linear (or convex) programming relaxation.
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