By Hanif D. Sherali,W. P. Adams

This booklet bargains with the idea 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 technique. In essence, the bridge among those different types 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 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 imperative thrust is to start with a version that presents an invaluable illustration and constitution, after which to additional increase this illustration via computerized reformulation and constraint iteration innovations. As pointed out above, the focus of this e-book is the improvement and alertness of RL T to be used as an automated reformulation method, and likewise, to generate robust legitimate inequalities. The RLT operates in levels. within the Reformulation section, particular types of extra implied polynomial constraints, that come with the aforementioned constraints with regards 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 specified situations, within the Linearization/Convexijication section. this is often performed through the definition of appropriate new variables to switch every one specified variable-product time period. the better dimensional illustration yields a linear (or convex) programming relaxation.

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A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems (Nonconvex Optimization and Its Applications) by Hanif D. Sherali,W. P. Adams

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