Inexact proximal Newton methods for self-concordant functions
نویسندگان
چکیده
منابع مشابه
Inexact proximal Newton methods for self-concordant functions
We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity patt...
متن کاملGeneralized Self-Concordant Functions: A Recipe for Newton-Type Methods
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The prop...
متن کاملComplexity of Inexact Proximal Newton methods
Recently several, so-called, proximal Newton methods were proposed for sparse optimization [6, 11, 8, 3]. These methods construct a composite quadratic approximation using Hessian information, optimize this approximation using a first-order method, such as coordinate descent and employ a line search to ensure sufficient descent. Here we propose a general framework, which includes slightly modif...
متن کاملSelf-adaptive inexact proximal point methods
We propose a class of self-adaptive proximal point methods suitable for degenerate optimization problems where multiple minimizers may exist, or where the Hessian may be singular at a local minimizer. If the proximal regularization parameter has the form μ(x)= β‖∇f (x)‖η where η ∈ [0,2) and β > 0 is a constant, we obtain convergence to the set of minimizers that is linear for η= 0 and β suffici...
متن کاملConvergence analysis of inexact proximal Newton-type methods
We study inexact proximal Newton-type methods to solve convex optimization problems in composite form: minimize x∈Rn f(x) := g(x) + h(x), where g is convex and continuously differentiable and h : R → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently. Proximal Newton-type methods require the solution of subproblems to obtain the search ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Methods of Operations Research
سال: 2016
ISSN: 1432-2994,1432-5217
DOI: 10.1007/s00186-016-0566-9