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A primal-dual potential reduction method for problems involving matrix inequalities
Interior point algorithms Linear matrix inequaliües Semidefinite programming
2015/8/11
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga ...
Variational Inequalities and Improved Convergence Rates for Tikhonov Regularisation on Banach Spaces
Variational Inequalities Improved Convergence Rates Tikhonov Regularisation Optimization and Control
2011/9/5
Abstract: In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach i...
Symmetries and adjunction inequalities for knot Floer homology
Symmetries adjunction inequalities knot Floer homology
2011/1/21
We derive symmetries and adjunction inequalities of the knot Floer homology groups which appear to be especially interesting for homologically essential knots.
Transportation cost inequalities for diffusions under uniform distance
Entropy (multi-valued) stochastic differential equations dissipative functions
2010/12/13
We prove the transportation inequality with the uniform norm for the laws of diffusion pro-
cesses with Lipschitz and/or dissipative coefficients and apply them to some singular stochastic differenti...
Bandwidth selection in kernel density estimation: oracle inequalities and adaptive minimax optimality
density estimation kernel estimators Lp–risk oracle inequalities adaptive estimation
2010/11/30
We address the problem of density estimation with L p–loss by selection of kernel estimators. We develop a selection procedure and derive corresponiding L p–risk oracle inequalities. It is shown that ...