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

By Hanif D. Sherali,W. P. Adams

This booklet offers with the idea and purposes of the Reformulation- Linearization/Convexification method (RL T) for fixing nonconvex optimization difficulties. A unified therapy of discrete and non-stop nonconvex programming difficulties is gifted utilizing this procedure. In essence, the bridge among those forms of nonconvexities is made through a polynomial illustration of discrete constraints. for instance, the binariness on a 0-1 variable x . may be equivalently J expressed because the polynomial constraint x . (1-x . ) = zero. the inducement for this booklet is J J the function of tight linear/convex programming representations or relaxations in fixing such discrete and non-stop nonconvex programming difficulties. The vital thrust is to start with a version that provides an invaluable illustration and constitution, after which to extra improve this illustration via automated reformulation and constraint iteration innovations. As pointed out above, the focus of this publication is the improvement and alertness of RL T to be used as an automated reformulation approach, and likewise, to generate robust legitimate inequalities. The RLT operates in levels. within the Reformulation part, 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 consequence linearized, other than that yes convex constraints are often retained in XV specific particular circumstances, within the Linearization/Convexijication part. this can be performed through the definition of compatible new variables to exchange every one precise variable-product time period. the better dimensional illustration yields a linear (or convex) programming relaxation.

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