A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information

Lv, Jian; Pang, Li-Ping; Meng, Fan-Yun

doi:10.1007/s10898-017-0565-2

Cited by 26 publications

(21 citation statements)

References 48 publications

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“…The 3D image of the objective function with n = 2 in Figure 1 shows that Our numerical results for minimizing F 1 (x) and F 2 (x) are reported in Tables 2 and 3, which show a reasonable comparison of Algorithm 1 to the penalty proximal bundle method (PBM) [31] and the inexact proximal bundle method (IPBM) [20].…”

Section: Cb2mentioning

confidence: 75%

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

Gao¹,

Lv²,

Wang³

et al. 2021

Journal of Industrial &Amp; Management Optimization

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We propose an alternating linearization bundle method for minimizing the sum of a nonconvex function and a convex function. The convex function is assumed to be "simple" in the sense that finding its proximal-like point is relatively easy. The nonconvex function is known through oracles which provide inexact information. The errors in function values and subgradient evaluations might be unknown, but are bounded by universal constants. We examine an alternating linearization bundle method in this setting and obtain reasonable convergence properties. Numerical results show the good performance of the method.

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Section: Cb2mentioning

confidence: 75%

“…All of them are taken from [19,30]. The second class of examples are taken from [9,10,20] which are the sum of a nonconvex function and a convex function.…”

Section: ≥¯mentioning

confidence: 99%

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

Gao¹,

Lv²,

Wang³

et al. 2021

Journal of Industrial &Amp; Management Optimization

Self Cite

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show abstract

“…minimizes objective function and constraint violation function separately. Because of its good results, filter technique has employed to many approaches, such as, sequential quadratic programming (SQP) methods [10], interior point approaches [6], bundle techniques [8] and SIP [9]. Although the filter method has promising numerical results, the structure of filter is complex.…”

Section: Sip : Minmentioning

confidence: 99%

A new adaptive method to nonlinear semi-infinite programming

Su¹,

Lin²,

Xu³

2022

JIMO

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<p style='text-indent:20px;'>In this paper, we propose a new adaptive method for solving nonlinear semi-infinite programming(SIP). In the presented method, the continuous infinite inequality constraints are transformed into equivalent equality constraints in integral form. Based on penalty method and trust region strategy, we propose a modified quadratic subproblem, in which an adaptive parameter is considered. The acceptable criterion of the trial point is adjustable according to the value of this adaptive parameter and the improvements that made by the current iteration. Compared with the existing methods, our method is more flexible. Under some reasonable conditions, the convergent properties of the proposed algorithm are proved. The numerical results are reported in the end.</p>

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“…In recent years, many scholars have devoted time to seeking effective methods for nonconvex and nonsmooth optimization problems, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Usually, bundle methods are much effective for solving nonsmooth optimization problems [21][22][23][24][25][26].…”

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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A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information

Cited by 26 publications

References 48 publications

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

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

A new adaptive method to nonlinear semi-infinite programming

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

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