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MP
2006
134views more  MP 2006»
13 years 4 months ago
Cubic regularization of Newton method and its global performance
In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme, we prove general local...
Yurii Nesterov, Boris T. Polyak
MP
2008
101views more  MP 2008»
13 years 4 months ago
Accelerating the cubic regularization of Newton's method on convex problems
In this paper we propose an accelerated version of the cubic regularization of Newton's method [6]. The original version, used for minimizing a convex function with Lipschitz...
Yu. Nesterov
JMLR
2010
143views more  JMLR 2010»
13 years 3 months ago
A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning
We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by ge...
Jin Yu, S. V. N. Vishwanathan, Simon Günter, ...
ICML
2007
IEEE
14 years 5 months ago
Scalable training of L1-regularized log-linear models
The l-bfgs limited-memory quasi-Newton method is the algorithm of choice for optimizing the parameters of large-scale log-linear models with L2 regularization, but it cannot be us...
Galen Andrew, Jianfeng Gao
JMIV
2007
83views more  JMIV 2007»
13 years 4 months ago
Minimization of a Detail-Preserving Regularization Functional for Impulse Noise Removal
Recently, a powerful two-phase method for restoring images corrupted with high level impulse noise has been developed. The main drawback of the method is the computational efficie...
Jian-Feng Cai, Raymond H. Chan, Carmine Di Fiore