Gradient projection methods for the $n$-coupling problem

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doi:10.4134/JKMS.j180517

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Gradient projection methods for the $n$-coupling problem

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positive definite matrix Gaussian measure $L^2$-Wasserstein least squares problem $n$-coupling problem Nesterov-Todd scaling gradient projection method

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초록

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the $n$-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

Abstract

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the $n$-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

참고문헌 (30)

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