By Hanif D. Sherali

This publication bargains with the speculation and functions of the Reformulation- Linearization/Convexification process (RL T) for fixing nonconvex optimization difficulties. A unified remedy of discrete and non-stop nonconvex programming difficulties is gifted utilizing this technique. 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 inducement for this publication is J J the function of tight linear/convex programming representations or relaxations in fixing such discrete and non-stop nonconvex programming difficulties. The important thrust is to start with a version that offers an invaluable illustration and constitution, after which to additional boost this illustration via automated reformulation and constraint iteration suggestions. As pointed out above, the focus of this booklet is the improvement 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 part, 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 accordingly linearized, other than that definite convex constraints are often retained in XV specific targeted circumstances, within the Linearization/Convexijication part. this can be performed through the definition of compatible new variables to switch every one particular variable-product time period. the better dimensional illustration yields a linear (or convex) programming leisure.

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