منابع مشابه
Extended Formulations in Mixed-Integer Convex Programming
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable wit...
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In this paper we consider the classical problem of finding a low rank approximation of a given matrix. In a least squares sense a closed form solution is available via factorization. However, with additional constraints, or in the presence of missing data, the problem becomes much more difficult. In this paper we show how to efficiently compute the convex envelopes of a class of rank minimizati...
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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...
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This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-a...
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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.
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ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 2013
ISSN: 0925-5001,1573-2916
DOI: 10.1007/s10898-013-0104-8