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Lower Bounds on Matrix Factorization Ranks via Noncommutative Polynomial Optimization
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نویسنده
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Gribling Sander ,Laat David de ,Laurent Monique
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منبع
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foundations of computational mathematics - 2019 - دوره : 19 - شماره : 5 - صفحه:1013 -1070
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چکیده
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We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. in particular, we consider the nonnegative rank, the positive semidefinite rank, and their symmetric analogs: the completely positive rank and the completely positive semidefinite rank. we study convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples.
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کلیدواژه
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Matrix factorization ranks ,Nonnegative rank ,Positive semidefinite rank ,Completely positive rank ,Completely positive semidefinite rank ,Noncommutative polynomial optimization ,15A48 ,15A23 ,90C22
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آدرس
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CWI, The Netherlands, CWI, The Netherlands, CWI, The Netherlands. Tilburg University, The Netherlands
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Authors
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