Convex optimization permutation

  • Is permutation matrix convex?

    The Birkhoff–von Neumann theorem says that every doubly stochastic real matrix is a convex combination of permutation matrices of the same order and the permutation matrices are precisely the extreme points of the set of doubly stochastic matrices..

  • What is the convex hull of a permutation?

    Given an ordered set of basis vectors Bu228.

    1. R2 with arbitrary order.
      2. Apply any permutation σi(B), it results in order of the basis.
      And I can cumulatively sum the basis with such order to form a set of vertices Vi.

  • The Birkhoff–von Neumann theorem says that every doubly stochastic real matrix is a convex combination of permutation matrices of the same order and the permutation matrices are precisely the extreme points of the set of doubly stochastic matrices.
We focus on optimization problems written over the set of permutations. While the relaxation tech- niques discussed in what follows are applicable to a much 
We write seriation as an optimization problem by proving the equivalence between the seriation and combinatorial 2-SUM problems on similarity matrices (2-SUM is 
We write seriation as an optimization problem by proving the equivalence between the seriation and combinatorial 2-SUM problems on similarity matrices (2-SUM 
The Birkhoff polytope (the convex hull of the set of permutation matrices) is frequently invoked in formulating relaxations of optimization problems over permutations. The Birkhoff polytope is represented using Θ(n2) variables and constraints, significantly more than the n variables one could use to represent a permutation as a vector.The Birkhoff polytope (the convex hull of the set of permutation matrices), which is represented using (n2) variables and constraints, is frequently invoked in for- mulating relaxations of optimization problems over permutations.

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Convex optimization for electrical engineering
Convex optimization
Convex optimization by stephen boyd and lieven vandenberghe
Bandit convex optimization towards tight bounds
Optimization under constraints
Convex optimization and applications
Convex optimization and concave
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Large-scale convex optimization via monotone operators
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Bandit convex optimization algorithm