RPCGB Method for Large-Scale Global Optimization Problems
In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditiona...
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| Published in | Axioms Vol. 12; no. 6; p. 603 |
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| Format | Journal Article |
| Language | English |
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| Abstract | In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency. |
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| AbstractList | In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency. |
| Audience | Academic |
| Author | El Mouatasim, Abdelkrim Ettahiri, Abderrahmane |
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| Cites_doi | 10.1109/LCOMM.2018.2875716 10.1007/s10208-015-9296-2 10.1016/j.jvcir.2013.01.010 10.1007/s11075-018-0471-9 10.1016/j.eneco.2018.12.022 10.3390/axioms11020042 10.1002/nav.3800030109 10.1016/j.jocs.2021.101451 10.2478/v10006-011-0024-z 10.1007/978-3-031-24041-6_18 10.1007/BF01100691 10.1109/ICASSP.2019.8683241 10.1007/978-1-4613-0279-7_31 10.1007/s10898-004-9972-2 10.3390/axioms11110607 10.1007/s00211-017-0916-4 10.1016/j.istruc.2021.11.012 10.1016/j.swevo.2018.04.008 10.1016/j.neucom.2015.04.033 10.1007/s11760-020-01696-2 10.1109/ICC.2019.8761120 10.3390/axioms11100551 10.1016/j.ins.2014.03.059 |
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| References | Ellaia (ref_26) 2011; 21 Kuang (ref_2) 2019; 80 Nanuclef (ref_12) 2014; 285 Ettahiri (ref_22) 2022; 22 Chan (ref_4) 2018; 138 ref_14 Amoura (ref_15) 2023; 317 ref_13 Li (ref_32) 2003; 219 ref_19 ref_17 Aslimani (ref_30) 2018; 79 Kaveh (ref_9) 2022; 35 Pogu (ref_18) 1994; 5 Benaissa (ref_16) 2021; 55 Frank (ref_23) 1956; 3 Oh (ref_5) 2013; 24 Zeng (ref_10) 2019; 44 ref_21 Baushev (ref_25) 2007; 2 Chu (ref_6) 2018; 22 ref_1 (ref_11) 2020; 14 Che (ref_31) 2015; 167 Touzin (ref_28) 2003; 14 ref_27 Pang (ref_3) 2015; 258 Nesterov (ref_20) 2017; 17 ref_8 Ali (ref_29) 2005; 31 Khamaru (ref_24) 2019; 20 ref_7 |
| References_xml | – volume: 22 start-page: 2535 year: 2018 ident: ref_6 article-title: Semi-blind millimeter-wave channel estimation using atomic norm minimization publication-title: IEEE Commun. doi: 10.1109/LCOMM.2018.2875716 – volume: 17 start-page: 527 year: 2017 ident: ref_20 article-title: Random gradient-free minimization of convex functions publication-title: Found. Comput. Math. doi: 10.1007/s10208-015-9296-2 – volume: 14 start-page: 5 year: 2003 ident: ref_28 article-title: On the Deng-Lin random number generators and related methods publication-title: Stat. Comput. – volume: 24 start-page: 332 year: 2013 ident: ref_5 article-title: Non-convex hybrid total variation for image denoising publication-title: J. Vis. Commun. Image Represent. doi: 10.1016/j.jvcir.2013.01.010 – volume: 79 start-page: 1021 year: 2018 ident: ref_30 article-title: A new chaos optimization algorithm based on symmetrization and levelling approaches for global optimization publication-title: Numer. Algorithms doi: 10.1007/s11075-018-0471-9 – volume: 20 start-page: 1 year: 2019 ident: ref_24 article-title: Convergence guarantees for a class of non-convex and non-smooth optimization problems publication-title: J. Mach. Learn. Res. – volume: 80 start-page: 123 year: 2019 ident: ref_2 article-title: Pricing in non-convex markets with quadratic deliverability costs publication-title: Energy Econ. doi: 10.1016/j.eneco.2018.12.022 – ident: ref_1 doi: 10.3390/axioms11020042 – volume: 3 start-page: 95 year: 1956 ident: ref_23 article-title: An Algorithm for Quadratic Programming publication-title: Naval Res. Logist. Q. doi: 10.1002/nav.3800030109 – volume: 258 start-page: 565 year: 2015 ident: ref_3 article-title: Risk management in portfolio applications of non-convex stochastic programming publication-title: Appl. Math. Comput. – volume: 219 start-page: 10909 year: 2003 ident: ref_32 article-title: An extension of the Fletcher Reeves method to linear equality constrained optimization problem publication-title: Appl. Math. Comput. – ident: ref_14 – volume: 55 start-page: 101451 year: 2021 ident: ref_16 article-title: YUKI Algorithm and POD-RBF for Elastostatic and Dynamic Crack Identification publication-title: J. Comput. Sci. doi: 10.1016/j.jocs.2021.101451 – volume: 21 start-page: 317 year: 2011 ident: ref_26 article-title: Random perturbation of projected variable metric method for linear constraints nonconvex nonsmooth optimization publication-title: Int. J. Appl. Math. Comput. Sci. doi: 10.2478/v10006-011-0024-z – volume: 317 start-page: 220 year: 2023 ident: ref_15 article-title: Deep Neural Network and YUKI Algorithm for Inner Damage Characterization Based on Elastic Boundary Displacement; Capozucca publication-title: Lect. Notes Civ. Eng. doi: 10.1007/978-3-031-24041-6_18 – volume: 5 start-page: 159 year: 1994 ident: ref_18 article-title: Global optimization by random perturbation of the gradient method with a fixed parameter publication-title: J. Glob. Optim. doi: 10.1007/BF01100691 – ident: ref_21 doi: 10.1109/ICASSP.2019.8683241 – ident: ref_27 doi: 10.1007/978-1-4613-0279-7_31 – volume: 2 start-page: 801 year: 2007 ident: ref_25 article-title: A multidimensional bisection method for minimizing function over simplex publication-title: Lect. Notes Eng. Comput. Sci. – volume: 31 start-page: 635 year: 2005 ident: ref_29 article-title: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems publication-title: J. Glob. Optim. doi: 10.1007/s10898-004-9972-2 – ident: ref_13 doi: 10.3390/axioms11110607 – volume: 138 start-page: 635 year: 2018 ident: ref_4 article-title: Convex non-convex image segmentation publication-title: Numer. Math. doi: 10.1007/s00211-017-0916-4 – volume: 35 start-page: 748 year: 2022 ident: ref_9 article-title: Improved arithmetic optimization algorithm and its application to discrete structural optimization publication-title: Structures doi: 10.1016/j.istruc.2021.11.012 – volume: 44 start-page: 320 year: 2019 ident: ref_10 article-title: Adaptive population extremal optimization-based PID neural network for multivariable nonlinear control systems publication-title: Swarm Evolut. Comput. doi: 10.1016/j.swevo.2018.04.008 – volume: 167 start-page: 569 year: 2015 ident: ref_31 article-title: An intelligent method of swarm neural networks forequalities constrained nonconvex optimization publication-title: Neurocomputing doi: 10.1016/j.neucom.2015.04.033 – volume: 14 start-page: 1565 year: 2020 ident: ref_11 article-title: Fast gradient descent algorithm for image classification with neural networks publication-title: Signal Image Video Process. doi: 10.1007/s11760-020-01696-2 – ident: ref_8 doi: 10.1109/ICC.2019.8761120 – ident: ref_7 doi: 10.3390/axioms11100551 – ident: ref_17 – ident: ref_19 – volume: 22 start-page: 142 year: 2022 ident: ref_22 article-title: Conditional gradient and bisection algorithms for non-convex optimization problem with random perturbation publication-title: Appl. Math. E-Notes – volume: 285 start-page: 66 year: 2014 ident: ref_12 article-title: A novel Frank-Wolfe algorithm. Analysis and applications to large-scale SVM training publication-title: Inf. Sci. doi: 10.1016/j.ins.2014.03.059 |
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| SubjectTerms | Algorithms Approximation bisection algorithm conditional gradient method Convex analysis Cost function Global optimization large-scale problem Linear programming Mathematical optimization Methods non-convex optimization Optimization techniques Perturbation random perturbation Random variables Signal processing Stochastic processes |
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| Title | RPCGB Method for Large-Scale Global Optimization Problems |
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