Extended Formulations for Polygons
نویسندگان
چکیده
منابع مشابه
Extended formulations for polygons
The extension complexity of a polytope P is the smallest integer k such that P is the projection of a polytope Q with k facets. We study the extension complexity of n-gons in the plane. First, we give a new proof that the extension complexity of regular n-gons is O(logn), a result originating from work by Ben-Tal and Nemirovski (Math. Oper. Res. 26(2), 193–205, 2001). Our proof easily generaliz...
متن کاملExtended Formulations for Sparsity Matroids
We show the existence of a polynomial-size extended formulation for the base polytope of a (k, l)-sparsity matroid. For an undirected graph G = (V,E), the size of the formulation is O(|V ||E|) when k ≥ l and O(|V ||E|) when k ≤ l. To this end, we employ the technique developed by Faenza et al. recently that uses a randomized communication protocol.
متن کاملStrong Reductions for Extended Formulations
We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [BPZ15] in two ways (1) relaxing the requirement of affineness, and (2) extending to fractional optimization problems. As applicationswe provide several newLP-hardness and SDP-hardness results, e.g., for theSparsestCut problem, the BalancedSeparator problem, the MaxCut problem and th...
متن کاملColumn generation for extended formulations
Working in an extended variable space allows one to develop tight reformulations for mixed integer programs. However, the size of the extended formulation grows rapidly too large for a direct treatment by a MIP-solver. Then, one can use projection tools and derive valid inequalities for the original formulation, or consider an approximate extended formulation (f.i., by aggregating variables). B...
متن کاملApproximate extended formulations
Mixed integer programming (MIP) formulations are typically tightened through the use of a separation algorithm and the addition of violated cuts. Using extended formulations involving new variables is a possible alternative, but this often results in prohibitively large MIPs where even the linear programming relaxations are hard or impossible to solve. In this paper, we demonstrate how, in cert...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2012
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-012-9421-9