Get A Reformulation-Linearization Technique for Solving Discrete PDF

By Hanif D. Sherali,W. P. Adams

This booklet bargains with the speculation and functions of the Reformulation- Linearization/Convexification strategy (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 sorts of nonconvexities is made through a polynomial illustration of discrete constraints. for instance, the binariness on a 0-1 variable x . could be equivalently J expressed because the polynomial constraint x . (1-x . ) = zero. the inducement for this publication is J J the position of tight linear/convex programming representations or relaxations in fixing such discrete and non-stop nonconvex programming difficulties. The imperative thrust is to begin with a version that gives an invaluable illustration and constitution, after which to additional enhance this illustration via automated reformulation and constraint new release strategies. As pointed out above, the focus of this booklet is the advance and alertness of RL T to be used as an automated reformulation method, and in addition, to generate robust legitimate inequalities. The RLT operates in levels. within the Reformulation section, specific sorts of extra implied polynomial constraints, that come with the aforementioned constraints relating to binary variables, are appended to the matter. The ensuing challenge is therefore linearized, other than that sure convex constraints are often retained in XV specific certain situations, within the Linearization/Convexijication section. this can be performed through the definition of compatible new variables to exchange every one unique variable-product time period. the better dimensional illustration yields a linear (or convex) programming relaxation.

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