Gradient-based algorithms for finding Nash equilibria in extensive form games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Exploiting equalities in polynomial programming
Operations Research Letters
Sparse non Gaussian component analysis by semidefinite programming
Machine Learning
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In this paper, we first demonstrate that positive semidefiniteness of a large well-structured sparse symmetric matrix can be represented via positive semidefiniteness of a bunch of smaller matrices linked, in a linear fashion, to the matrix. We derive also the “dual counterpart” of the outlined representation, which expresses the possibility of positive semidefinite completion of a well-structured partially defined symmetric matrix in terms of positive semidefiniteness of a specific bunch of fully defined submatrices of the matrix. Using the representations, we then reformulate well-structured large-scale semidefinite problems into smooth convex–concave saddle point problems, which can be solved by a Prox-method developed in [6] with efficiency $$\mathcal {O}(\epsilon^{-1})$$. Implementations and some numerical results for large-scale Lovász capacity and MAXCUT problems are finally presented.