An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information

Gao, Hui; Lv, Jian; Wang, Xiaoliang; Pang, Li-Ping

doi:10.3934/jimo.2019135

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…Then, bundle techniques can be a class of possible effective ways to deal with the composite problem (1). At present, the proximal alternating linearization type methods (see [4,[27][28][29]) are one effective kind of bundle methods for some composite problems. They need to solve two subproblems at each iteration and the data referred are usually exact.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization

Wang

Pang

et al. 2021

Mathematics

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In this paper, an adaptive proximal bundle method is proposed for a class of nonconvex and nonsmooth composite problems with inexact information. The composite problems are the sum of a finite convex function with inexact information and a nonconvex function. For the nonconvex function, we design the convexification technique and ensure the linearization errors of its augment function to be nonnegative. Then, the sum of the convex function and the augment function is regarded as an approximate function to the primal problem. For the approximate function, we adopt a disaggregate strategy and regard the sum of cutting plane models of the convex function and the augment function as a cutting plane model for the approximate function. Then, we give the adaptive nonconvex proximal bundle method. Meanwhile, for the convex function with inexact information, we utilize the noise management strategy and update the proximal parameter to reduce the influence of inexact information. The method can obtain an approximate solution. Two polynomial functions and six DC problems are referred to in the numerical experiment. The preliminary numerical results show that our algorithm is effective and reliable.

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Section: Introductionmentioning

confidence: 99%

An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization

Wang

Pang

et al. 2021

Mathematics

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A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

Wang

Pang

2021

Asia Pac. J. Oper. Res.

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The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

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Proximal decomposition of convex optimization via an alternating linearization algorithm with inexact oracles

Huang,

He,

Qiao

et al. 2024

JIMO

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An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information

Cited by 3 publications

References 27 publications

An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization

An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization

A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

Proximal decomposition of convex optimization via an alternating linearization algorithm with inexact oracles

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