Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization
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DOI: 10.1007/s10957-007-9335-5
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- Robert Mifflin, 1977. "An Algorithm for Constrained Optimization with Semismooth Functions," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 191-207, May.
- A. Bagirov & A. Rubinov & N. Soukhoroukova & J. Yearwood, 2003. "Unsupervised and supervised data classification via nonsmooth and global optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 1-75, June.
- E. Polak & J. O. Royset, 2003. "Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 421-457, December.
- Bagirov, Adil M. & Yearwood, John, 2006. "A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems," European Journal of Operational Research, Elsevier, vol. 170(2), pages 578-596, April.
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Cited by:
- Adil M. Bagirov & Julien Ugon & Hijran G. Mirzayeva, 2015. "Nonsmooth Optimization Algorithm for Solving Clusterwise Linear Regression Problems," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 755-780, March.
- Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
- A. Bagirov & B. Ordin & G. Ozturk & A. Xavier, 2015. "An incremental clustering algorithm based on hyperbolic smoothing," Computational Optimization and Applications, Springer, vol. 61(1), pages 219-241, May.
- A. Bagirov & J. Ugon, 2011. "Codifferential method for minimizing nonsmooth DC functions," Journal of Global Optimization, Springer, vol. 50(1), pages 3-22, May.
- A. M. Bagirov & L. Jin & N. Karmitsa & A. Al Nuaimat & N. Sultanova, 2013. "Subgradient Method for Nonconvex Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 416-435, May.
- Chad Davis & Warren Hare, 2013. "Exploiting Known Structures to Approximate Normal Cones," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 665-681, November.
- Shuai Liu, 2019. "A simple version of bundle method with linear programming," Computational Optimization and Applications, Springer, vol. 72(2), pages 391-412, March.
- Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
- Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
- Kalyanmoy Deb & Shivam Gupta & Joydeep Dutta & Bhoomija Ranjan, 2013. "Solving dual problems using a coevolutionary optimization algorithm," Journal of Global Optimization, Springer, vol. 57(3), pages 891-933, November.
- Adil Bagirov & Julien Ugon & Dean Webb & Gurkan Ozturk & Refail Kasimbeyli, 2013. "A novel piecewise linear classifier based on polyhedral conic and max–min separabilities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 3-24, April.
- Gaudioso, Manlio & Giallombardo, Giovanni & Mukhametzhanov, Marat, 2018. "Numerical infinitesimals in a variable metric method for convex nonsmooth optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 312-320.
- Napsu Karmitsa, 2016. "Testing Different Nonsmooth Formulations of the Lennard–Jones Potential in Atomic Clustering Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 316-335, October.
- K. C. Kiwiel, 2010. "Improved Convergence Result for the Discrete Gradient and Secant Methods for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 69-75, January.
- Adil Bagirov & Asef Ganjehlou, 2008. "An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 187-206, April.
- M. V. Dolgopolik, 2018. "A convergence analysis of the method of codifferential descent," Computational Optimization and Applications, Springer, vol. 71(3), pages 879-913, December.
- Nezam Mahdavi-Amiri & Rohollah Yousefpour, 2012. "An Effective Nonsmooth Optimization Algorithm for Locally Lipschitz Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 180-195, October.
- M. Golestani & H. Sadeghi & Y. Tavan, 2018. "Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 896-916, December.
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Keywords
Nonsmooth optimization; Derivative-free optimization; Subdifferentials; Discrete gradients;All these keywords.
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