Read e-book online A Reformulation-Linearization Technique for Solving Discrete PDF

By Hanif D. Sherali,W. P. Adams

This ebook offers with the idea and purposes of the Reformulation- Linearization/Convexification procedure (RL T) for fixing nonconvex optimization difficulties. A unified therapy of discrete and non-stop nonconvex programming difficulties is gifted utilizing this method. In essence, the bridge among those varieties of nonconvexities is made through a polynomial illustration of discrete constraints. for instance, the binariness on a 0-1 variable x . might 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 critical thrust is to begin with a version that gives an invaluable illustration and constitution, after which to additional boost this illustration via computerized reformulation and constraint new release strategies. As pointed out above, the point of interest of this booklet is the advance 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 section, particular types of extra implied polynomial constraints, that come with the aforementioned constraints in terms of binary variables, are appended to the matter. The ensuing challenge is hence linearized, other than that sure convex constraints are often retained in XV specific specific circumstances, within the Linearization/Convexijication part. this can be performed through the definition of appropriate new variables to interchange every one unique 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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