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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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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.
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참고문헌 (30)
참고문헌 신청
M. Agueh / 2011 / Barycenters in the Wasserstein space / SIAM J. Math. Anal 43(2):904~924
P. C. Alvarez Esteban / 2016 / A fixed-point approach to barycenters in Wasserstein space / J. Math. Anal. Appl 441:744~762
M. Bacak / 2014 / Computing medians and means in Hadamard spaces / SIAM J. Optim 24(3):1542~1566
D. P. Bertsekas / 1999 / Nonlinear Programming, Athena Scientific Optimization and Computation Series / Athena Scientific
D. P. Bertsekas / 2015 / Incremental gradient, subgradient, and proximal methods for convex optimiza-tion: A survey / Preprint arXiv:1507.01030
P. C. Alvarez Esteban / 2016 / A fixed-point approach to barycenters in Wasserstein space / J. Math. Anal. Appl 441:744~762
M. Bacak / 2014 / Computing medians and means in Hadamard spaces / SIAM J. Optim 24(3):1542~1566
D. P. Bertsekas / 1999 / Nonlinear Programming, Athena Scientific Optimization and Computation Series / Athena Scientific
D. P. Bertsekas / 2015 / Incremental gradient, subgradient, and proximal methods for convex optimiza-tion: A survey / Preprint arXiv:1507.01030
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