
Data Structures for Representing Symmetry in Quadratically Constrained Quadratic Programs
Symmetry in mathematical programming may lead to a multiplicity of solut...
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Tighter LiftingFree Convex Relaxations for Quadratic Matching Problems
In this work we study convex relaxations of quadratic optimisation probl...
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A simple Newton method for local nonsmooth optimization
Superlinear convergence has been an elusive goal for blackbox nonsmooth...
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RockIt: Exploiting Parallelism and Symmetry for MAP Inference in Statistical Relational Models
RockIt is a maximum aposteriori (MAP) query engine for statistical rela...
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Towards Verified Stochastic Variational Inference for Probabilistic Programs
Probabilistic programming is the idea of writing models from statistics ...
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Improving problem solving by exploiting the concept of symmetry
We investigate the concept of symmetry and its role in problem solving. ...
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Lifted Convex Quadratic Programming
Symmetry is the essential element of lifted inference that has recently demon strated the possibility to perform very efficient inference in highlyconnected, but symmetric probabilistic models models. This raises the question, whether this holds for optimisation problems in general. Here we show that for a large class of optimisation methods this is actually the case. More precisely, we introduce the concept of fractional symmetries of convex quadratic programs (QPs), which lie at the heart of many machine learning approaches, and exploit it to lift, i.e., to compress QPs. These lifted QPs can then be tackled with the usual optimization toolbox (offtheshelf solvers, cutting plane algorithms, stochastic gradients etc.). If the original QP exhibits symmetry, then the lifted one will generally be more compact, and hence their optimization is likely to be more efficient.
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