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SIAMJO
2000
67views more  SIAMJO 2000»
13 years 4 months ago
Gradient Convergence in Gradient methods with Errors
We consider the gradient method xt+1 = xt + t(st + wt), where st is a descent direction of a function f : n and wt is a deterministic or stochastic error. We assume that f is Lip...
Dimitri P. Bertsekas, John N. Tsitsiklis
CDC
2010
IEEE
196views Control Systems» more  CDC 2010»
13 years 1 days ago
Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema
The asymptotic behavior of stochastic gradient algorithms is studied. Relying on some results of differential geometry (Lojasiewicz gradient inequality), the almost sure pointconve...
Vladislav B. Tadic
MP
2010
162views more  MP 2010»
13 years 3 months ago
Approximation accuracy, gradient methods, and error bound for structured convex optimization
Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of i...
Paul Tseng
SIAMIS
2011
12 years 12 months ago
Gradient-Based Methods for Sparse Recovery
The convergence rate is analyzed for the sparse reconstruction by separable approximation (SpaRSA) algorithm for minimizing a sum f(x) + ψ(x), where f is smooth and ψ is convex, ...
William W. Hager, Dzung T. Phan, Hongchao Zhang
AUTOMATICA
2006
76views more  AUTOMATICA 2006»
13 years 5 months ago
Nonlinear robust performance analysis using complex-step gradient approximation
In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The m...
Jongrae Kim, Declan G. Bates, Ian Postlethwaite