McCormick-Based Relaxations of Algorithms
نویسندگان
چکیده
منابع مشابه
McCormick-Based Relaxations of Algorithms
Theory and implementation for the global optimization of a wide class of algorithms is presented via convex/affine relaxations. The basis for the proposed relaxations is the systematic construction of subgradients for the convex relaxations of factorable functions by McCormick [Math. Prog., 10 (1976), pp. 147–175]. Similar to the convex relaxation, the subgradient propagation relies on the recu...
متن کاملMultivariate McCormick relaxations
McCormick (Math Prog 10(1):147–175, 1976) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F◦ f , where F is a univariate function. Herein, the composition theorem is generalized to allowmultivariate outer functions F , and theory for the propagation of subgradients is presented. The generalization...
متن کاملDifferentiable McCormick relaxations
McCormick’s classical relaxation technique constructs closed-form convex and concave relaxations of compositions of simple intrinsic functions. These relaxations have several properties which make them useful for lower bounding problems in global optimization: they can be evaluated automatically, accurately, and computationally inexpensively, and they converge rapidly to the relaxed function as...
متن کاملReverse propagation of McCormick relaxations
Constraint propagation techniques have heavily utilized interval arithmetic while the application of convex and concave relaxations has been mostly restricted to the domain of global optimization. Here, reverse McCormick propagation, a method to construct and improve McCormick relaxations using a directed acyclic graph representation of the constraints, is proposed. In particular, this allows t...
متن کاملTightening piecewise McCormick relaxations for bilinear problems
We address nonconvex bilinear problems where the main objective is the computation of a tight lower bound for the objective function to be minimized. This can be obtained through a mixed-integer linear programming formulation relying on the concept of piecewise McCormick relaxation. It works by dividing the domain of one of the variables in each bilinear term into a given number of partitions, ...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2009
ISSN: 1052-6234,1095-7189
DOI: 10.1137/080717341