Inexact Variants of the Proximal Point Algorithm without Monotonicity
نویسندگان
چکیده
منابع مشابه
Inexact Variants of the Proximal Point Algorithm without Monotonicity
This paper studies convergence properties of inexact variants of the proximal point algorithm when applied to a certain class of nonmonotone mappings. The presented algorithms allow for constant relative errors, in the line of the recently proposed hybrid proximal-extragradient algorithm. The main convergence result extends a recent work of the second author, where exact solutions for the proxi...
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The proximal point algorithm (PPA) is classical and popular in the community of Optimization. In practice, inexact PPAs which solves the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact PPA with a new inexact criterion for solving convex minimization, and show that the iteration-complexity of this...
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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...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2003
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623401399587