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Monotonic Optimization: Branch and Cut Methods
2005Monotonic optimization is concerned with optimization problems dealing with multivariate monotonic functions and differences of monotonic functions. For the study of this class of problems a general framework (Tuy, 2000a) has been earlier developed where a key role was given to a separation property of solution sets of monotonic inequalities similar to
Hoang Tuy +2 more
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Isolation branching: a branch and bound algorithm for the k-terminal cut problem
Journal of Combinatorial Optimization, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mark Velednitsky, Dorit S. Hochbaum
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Branch, Cut, and Price: Sequential and Parallel
2001Branch, cut, and price (BCP) is an LP-based branch and bound technique for solving large-scale discrete optimization problems (DOPs). In BCP, both cuts and variables can be generated dynamically throughout the search tree. The ability to handle constantly changing sets of cuts and variables allows these algorithms to undertake the solution of very ...
Laszlo Ladányi +2 more
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Multivalued Functions, Branch Points, and Cuts
2007Because ei2π = 1, it is straightforward to see that if the argument of a complex variable z is increased by 2π, one obtains the same value of the complex variable. That is, for a given r and θ, we write $$ z(r,\theta ) = re^{i\theta } $$ (6.1a) Then $$ z(r,\theta + 2\pi ) = re^{i\theta } e^{2i\pi } = re^{i\theta } = z(r,\theta ) $$ (6 ...
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Branch-and-Cut algorithm for the connected-cut problem
2014Let G=(V,E) be an undirected connected graph. Let W be a subset of V, distinct from V. The set W is said proper when it is non-empty. We denote by δ(W), the set of edges of E having exactly one endnode in W. A set F is called a cut of G, if there exists a proper subset W of V such that F=δ(W).
Borne, Sylvie +4 more
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Machine Learning Techniques for Branch-and-Cut Methods: The Selection of Cutting Planes
The selection of cuts to be added to the current LP relaxation is one of the most critical task in Branch-and-Cut methods, since it strongly affects the performances of the algorithm. Recently, machine learning techniques have become popular to define effective cut selection strategies.Giovanni Giallombardo +2 more
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