dc programming
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2022 ◽  
Vol 40 ◽  
pp. 1-16
Author(s):  
Fakhrodin Hashemi ◽  
Saeed Ketabchi

Optimal correction of an infeasible equations system as Ax + B|x|= b leads into a non-convex fractional problem. In this paper, a regularization method(ℓp-norm, 0 < p < 1), is presented to solve mentioned fractional problem. In this method, the obtained problem can be formulated as a non-convex and nonsmooth optimization problem which is not Lipschitz. The objective function of this problem can be decomposed as a difference of convex functions (DC). For this reason, we use a special smoothing technique based on DC programming. The numerical results obtained for generated problem show high performance and the effectiveness of the proposed method.


Author(s):  
Chih-Sheng Chuang ◽  
Hongjin He ◽  
Zhiyuan Zhang
Keyword(s):  

Author(s):  
ramzi kasri ◽  
fatima bellahcene

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our solution method is a combination between the multiobjective approach and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers’ preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC programming and DC algorithm. A numerical example is included for illustration.


Author(s):  
Tao Pham Dinh ◽  
Van Ngai Huynh ◽  
Hoai An Le Thi ◽  
Vinh Thanh Ho
Keyword(s):  

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jie Shen ◽  
Na Xu ◽  
Fang-Fang Guo ◽  
Han-Yang Li ◽  
Pan Hu

Abstract For nonlinear nonsmooth DC programming (difference of convex functions), we introduce a new redistributed proximal bundle method. The subgradient information of both the DC components is gathered from some neighbourhood of the current stability center and it is used to build separately an approximation for each component in the DC representation. Especially we employ the nonlinear redistributed technique to model the second component of DC function by constructing a local convexification cutting plane. The corresponding convexification parameter is adjusted dynamically and is taken sufficiently large to make the ”augmented” linearization errors nonnegative. Based on above techniques we obtain a new convex cutting plane model of the original objective function. Based on this new approximation the redistributed proximal bundle method is designed and the convergence of the proposed algorithm to a Clarke stationary point is proved. A simple numerical experiment is given to show the validity of the presented algorithm.


2021 ◽  
Author(s):  
Annabella Astorino ◽  
Massimo Di Francesco ◽  
Manlio Gaudioso ◽  
Enrico Gorgone ◽  
Benedetto Manca

AbstractWe consider polyhedral separation of sets as a possible tool in supervised classification. In particular, we focus on the optimization model introduced by Astorino and Gaudioso (J Optim Theory Appl 112(2):265–293, 2002) and adopt its reformulation in difference of convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of the implementation of DCA on a number of benchmark classification datasets.


Author(s):  
Thi Thuy Tran ◽  
Hoai An Pham Thi ◽  
Tao Pham Dinh ◽  
Nhu Tuan Nguyen

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Hao-Hsuan Chang ◽  
Lingjia Liu ◽  
Jianan Bai ◽  
Alex Pidwerbetsky ◽  
Allan Berlinsky ◽  
...  

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