Cubic-regularization counterpart of a variable-norm trust-region method for unconstrained minimization
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DOI: 10.1007/s10898-016-0475-8
Abstract: In a recent paper, we introduced a trust-region method with variable norms for unconstrained minimization, we proved standard asymptotic convergence results, and we discussed the impact of this method in global optimization. Here we will… read more here.
Keywords: cubic regularization; unconstrained minimization; method; trust region ... See more keywords
On global minimizers of quadratic functions with cubic regularization
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DOI: 10.1007/s11590-018-1316-0
Abstract: In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in… read more here.
Keywords: quadratic functions; global minimizers; minimizers quadratic; cubic regularization ... See more keywords
Cubic Regularization Methods with Second-Order Complexity Guarantee Based on a New Subproblem Reformulation
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DOI: 10.1007/s40305-022-00398-5
Abstract: The cubic regularization (CR) algorithm has attracted a lot of attentions in the literature in recent years. We propose a new reformulation of the cubic regularization subproblem. The reformulation is an unconstrained convex problem that… read more here.
Keywords: subproblem reformulation; complexity; regularization; reformulation ... See more keywords
Stochastic analysis of an adaptive cubic regularization method under inexact gradient evaluations and dynamic Hessian accuracy
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DOI: 10.1080/02331934.2021.1892104
Abstract: We here adapt an extended version of the adaptive cubic regularization method with dynamic inexact Hessian information for nonconvex optimization in Bellavia et al. [Adaptive cubic regularization methods with dynamic inexact hessian information and applications… read more here.
Keywords: analysis; regularization method; cubic regularization; adaptive cubic ... See more keywords