A Reformulation-Linearization Technique for Solving Discrete by Hanif D. Sherali,W. P. Adams

By Hanif D. Sherali,W. P. Adams

This ebook bargains with the speculation and purposes of the Reformulation- Linearization/Convexification approach (RL T) for fixing nonconvex optimization difficulties. A unified remedy of discrete and non-stop nonconvex programming difficulties is gifted utilizing this strategy. In essence, the bridge among those sorts of nonconvexities is made through a polynomial illustration of discrete constraints. for instance, the binariness on a 0-1 variable x . should be equivalently J expressed because the polynomial constraint x . (1-x . ) = zero. the incentive for this ebook is J J the function of tight linear/convex programming representations or relaxations in fixing such discrete and non-stop nonconvex programming difficulties. The central thrust is to begin with a version that gives an invaluable illustration and constitution, after which to additional develop this illustration via computerized reformulation and constraint iteration suggestions. As pointed out above, the focus of this publication is the advance and alertness of RL T to be used as an automated reformulation approach, and in addition, to generate powerful legitimate inequalities. The RLT operates in stages. within the Reformulation section, specific sorts of extra implied polynomial constraints, that come with the aforementioned constraints on the subject of binary variables, are appended to the matter. The ensuing challenge is as a result linearized, other than that convinced convex constraints are often retained in XV specific targeted instances, within the Linearization/Convexijication part. this can be performed through the definition of compatible new variables to interchange every one distinctive variable-product time period. the better dimensional illustration yields a linear (or convex) programming relaxation.

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