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The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems

Citations

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Cited by:

  1. Karima Boufi & Mostafa El Haffari & Ahmed Roubi, 2020. "Optimality Conditions and a Method of Centers for Minimax Fractional Programs with Difference of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 105-132, October.
  2. Hoai Thi & Duc Tran, 2014. "New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains," Journal of Global Optimization, Springer, vol. 60(1), pages 5-24, September.
  3. Marah-Lisanne Thormann & Phan Tu Vuong & Alain B. Zemkoho, 2024. "The Boosted Difference of Convex Functions Algorithm for Value-at-Risk Constrained Portfolio Optimization," Papers 2402.09194, arXiv.org.
  4. Pietro D’Alessandro & Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2024. "The Descent–Ascent Algorithm for DC Programming," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 657-671, March.
  5. M. Alimohammady & M. Ramazannejad, 2016. "Inertial proximal algorithm for difference of two maximal monotone operators," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 1-8, March.
  6. Min Tao & Jiang-Ning Li, 2023. "Error Bound and Isocost Imply Linear Convergence of DCA-Based Algorithms to D-Stationarity," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 205-232, April.
  7. Hoai An Thi & Thi Minh Tam Nguyen & Tao Pham Dinh, 2023. "On solving difference of convex functions programs with linear complementarity constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 163-197, September.
  8. H. Le Thi & A. Vaz & L. Vicente, 2012. "Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 190-214, April.
  9. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
  10. Jean-Paul Penot, 2011. "The directional subdifferential of the difference of two convex functions," Journal of Global Optimization, Springer, vol. 49(3), pages 505-519, March.
  11. Hoai Le Thi & Hoai Le & Tao Pham Dinh & Ngai Van Huynh, 2013. "Binary classification via spherical separator by DC programming and DCA," Journal of Global Optimization, Springer, vol. 56(4), pages 1393-1407, August.
  12. Tao Pham Dinh & Van Ngai Huynh & Hoai An Le Thi & Vinh Thanh Ho, 2022. "Alternating DC algorithm for partial DC programming problems," Journal of Global Optimization, Springer, vol. 82(4), pages 897-928, April.
  13. Yujie Li & Benying Tan & Atsunori Kanemura & Shuxue Ding & Wuhui Chen, 2018. "Analysis Sparse Representation for Nonnegative Signals Based on Determinant Measure by DC Programming," Complexity, Hindawi, vol. 2018, pages 1-12, April.
  14. Hoai Le Thi & Duc Tran, 2014. "Optimizing a multi-stage production/inventory system by DC programming based approaches," Computational Optimization and Applications, Springer, vol. 57(2), pages 441-468, March.
  15. Tao Pham Dinh & Yi-Shuai Niu, 2011. "An efficient DC programming approach for portfolio decision with higher moments," Computational Optimization and Applications, Springer, vol. 50(3), pages 525-554, December.
  16. Hoai An, Le Thi & Phuc, Nguyen Trong & Tao, Pham Dinh, 2007. "A continuous DC programming approach to the strategic supply chain design problem from qualified partner set," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1001-1012, December.
  17. Hoai An Le Thi & Mahdi Moeini, 2014. "Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 199-224, April.
  18. Hoai Le Thi & Tao Pham Dinh & Huynh Ngai, 2012. "Exact penalty and error bounds in DC programming," Journal of Global Optimization, Springer, vol. 52(3), pages 509-535, March.
  19. Hoai An Le Thi & Manh Cuong Nguyen, 2017. "DCA based algorithms for feature selection in multi-class support vector machine," Annals of Operations Research, Springer, vol. 249(1), pages 273-300, February.
  20. Mahdi Moeini, 2022. "Solving the index tracking problem: a continuous optimization approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 807-835, June.
  21. Joaquim Júdice, 2012. "Algorithms for linear programming with linear complementarity constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 4-25, April.
  22. Carrizosa, Emilio & Goerigk, Marc & Schöbel, Anita, 2017. "A biobjective approach to recoverable robustness based on location planning," European Journal of Operational Research, Elsevier, vol. 261(2), pages 421-435.
  23. David Wozabal, 2012. "A framework for optimization under ambiguity," Annals of Operations Research, Springer, vol. 193(1), pages 21-47, March.
  24. A. Astorino & A. Fuduli & M. Gaudioso, 2010. "DC models for spherical separation," Journal of Global Optimization, Springer, vol. 48(4), pages 657-669, December.
  25. Annabella Astorino & Antonio Fuduli & Manlio Gaudioso, 2012. "Margin maximization in spherical separation," Computational Optimization and Applications, Springer, vol. 53(2), pages 301-322, October.
  26. Hoai An Le Thi & Van Ngai Huynh & Tao Pham Dinh, 2018. "Convergence Analysis of Difference-of-Convex Algorithm with Subanalytic Data," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 103-126, October.
  27. João Carlos O. Souza & Paulo Roberto Oliveira & Antoine Soubeyran, 2016. "Global convergence of a proximal linearized algorithm for difference of convex functions," Post-Print hal-01440298, HAL.
  28. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2023. "Sparse optimization via vector k-norm and DC programming with an application to feature selection for support vector machines," Computational Optimization and Applications, Springer, vol. 86(2), pages 745-766, November.
  29. A. B. Dieker & S. Ghosh & M. S. Squillante, 2017. "Optimal Resource Capacity Management for Stochastic Networks," Operations Research, INFORMS, vol. 65(1), pages 221-241, February.
  30. Manuel Ruiz & Olivier Briant & Jean-Maurice Clochard & Bernard Penz, 2013. "Large-scale standard pooling problems with constrained pools and fixed demands," Journal of Global Optimization, Springer, vol. 56(3), pages 939-956, July.
  31. L. Abdallah & M. Haddou & T. Migot, 2019. "A sub-additive DC approach to the complementarity problem," Computational Optimization and Applications, Springer, vol. 73(2), pages 509-534, June.
  32. Yuan, Quan & Liu, Binghui, 2021. "Community detection via an efficient nonconvex optimization approach based on modularity," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
  33. Liming Yang & Laisheng Wang, 2013. "A class of semi-supervised support vector machines by DC programming," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 417-433, December.
  34. Mahide Küçük & Didem Tozkan & Yalçın Küçük, 2017. "On some geometric conditions for minimality of DCH-functions via DC-duality approach," Journal of Global Optimization, Springer, vol. 69(4), pages 951-965, December.
  35. Xiang Zhang & Yichao Wu & Lan Wang & Runze Li, 2016. "Variable selection for support vector machines in moderately high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 53-76, January.
  36. Abbaszadehpeivasti, Hadi, 2024. "Performance analysis of optimization methods for machine learning," Other publications TiSEM 3050a62d-1a1f-494e-99ef-7, Tilburg University, School of Economics and Management.
  37. Laura Girometti & Martin Huska & Alessandro Lanza & Serena Morigi, 2024. "Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1286-1325, September.
  38. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
  39. Hoai Le Thi & Van Huynh & Tao Dinh & A. Vaz & L. Vicente, 2014. "Globally convergent DC trust-region methods," Journal of Global Optimization, Springer, vol. 59(2), pages 209-225, July.
  40. F. Mashkoorzadeh & N. Movahedian & S. Nobakhtian, 2022. "The DTC (difference of tangentially convex functions) programming: optimality conditions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 270-295, July.
  41. Hoai An Le Thi & Vinh Thanh Ho & Tao Pham Dinh, 2019. "A unified DC programming framework and efficient DCA based approaches for large scale batch reinforcement learning," Journal of Global Optimization, Springer, vol. 73(2), pages 279-310, February.
  42. Gruzdeva, Tatiana V. & Strekalovsky, Alexander S., 2018. "On solving the sum-of-ratios problem," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 260-269.
  43. Albert Ferrer & Adil Bagirov & Gleb Beliakov, 2015. "Solving DC programs using the cutting angle method," Journal of Global Optimization, Springer, vol. 61(1), pages 71-89, January.
  44. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2015. "Optimal Replenishment Order Placement in a Finite Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1078-1089, March.
  45. Julien Schleich & Hoai An Le Thi & Pascal Bouvry, 2012. "Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 397-412, November.
  46. Crystal T. Nguyen & Daniel J. Luckett & Anna R. Kahkoska & Grace E. Shearrer & Donna Spruijt‐Metz & Jaimie N. Davis & Michael R. Kosorok, 2020. "Estimating individualized treatment regimes from crossover designs," Biometrics, The International Biometric Society, vol. 76(3), pages 778-788, September.
  47. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
  48. Marcia Fampa & Jon Lee & Wendel Melo, 2017. "On global optimization with indefinite quadratics," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 309-337, September.
  49. Hoai An, Le Thi & Minh, Le Hoai & Tao, Pham Dinh, 2007. "Optimization based DC programming and DCA for hierarchical clustering," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1067-1085, December.
  50. Marcoux, Mathieu & Russell, Thomas M. & Wan, Yuanyuan, 2024. "A simple specification test for models with many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 242(1).
  51. Jeon, Jong-June & Kwon, Sunghoon & Choi, Hosik, 2017. "Homogeneity detection for the high-dimensional generalized linear model," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 61-74.
  52. Lin Zhang & Andrew DiLernia & Karina Quevedo & Jazmin Camchong & Kelvin Lim & Wei Pan, 2021. "A random covariance model for bi‐level graphical modeling with application to resting‐state fMRI data," Biometrics, The International Biometric Society, vol. 77(4), pages 1385-1396, December.
  53. M. Bierlaire & M. Thémans & N. Zufferey, 2010. "A Heuristic for Nonlinear Global Optimization," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 59-70, February.
  54. Nilay Noyan & Gábor Rudolf, 2013. "Optimization with Multivariate Conditional Value-at-Risk Constraints," Operations Research, INFORMS, vol. 61(4), pages 990-1013, August.
  55. Hoai Le Thi & Mahdi Moeini & Tao Pham Dinh & Joaquim Judice, 2012. "A DC programming approach for solving the symmetric Eigenvalue Complementarity Problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1097-1117, April.
  56. Outi Montonen & Kaisa Joki, 2018. "Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints," Journal of Global Optimization, Springer, vol. 72(3), pages 403-429, November.
  57. Strekalovsky, Alexander S., 2015. "On local search in d.c. optimization problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 73-83.
  58. Ye He & Ling Zhou & Yingcun Xia & Huazhen Lin, 2023. "Center‐augmented ℓ2‐type regularization for subgroup learning," Biometrics, The International Biometric Society, vol. 79(3), pages 2157-2170, September.
  59. Hoai An Le Thi & Thi Tuyet Trinh Nguyen & Hoang Phuc Hau Luu, 2022. "A DC programming approach for solving a centralized group key management problem," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3165-3193, December.
  60. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.
  61. Yoshihiro Kanno, 2018. "Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach," Computational Optimization and Applications, Springer, vol. 71(2), pages 403-433, November.
  62. Jun Sun & Wentao Qu, 2022. "DCA for Sparse Quadratic Kernel-Free Least Squares Semi-Supervised Support Vector Machine," Mathematics, MDPI, vol. 10(15), pages 1-17, August.
  63. Marcia Fampa & Francisco Pinillos Nieto, 2018. "Extensions on ellipsoid bounds for quadratic integer programming," Journal of Global Optimization, Springer, vol. 71(3), pages 457-482, July.
  64. M. V. Dolgopolik, 2022. "DC Semidefinite programming and cone constrained DC optimization I: theory," Computational Optimization and Applications, Springer, vol. 82(3), pages 649-671, July.
  65. Tao Pham Dinh & Nam Nguyen Canh & Hoai Le Thi, 2010. "An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs," Journal of Global Optimization, Springer, vol. 48(4), pages 595-632, December.
  66. Hadi Abbaszadehpeivasti & Etienne Klerk & Moslem Zamani, 2024. "On the Rate of Convergence of the Difference-of-Convex Algorithm (DCA)," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 475-496, July.
  67. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico & Adil M. Bagirov, 2018. "Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations," Journal of Global Optimization, Springer, vol. 71(1), pages 37-55, May.
  68. Liping Pang & Xiaoliang Wang & Fanyun Meng, 2023. "A proximal bundle method for a class of nonconvex nonsmooth composite optimization problems," Journal of Global Optimization, Springer, vol. 86(3), pages 589-620, July.
  69. Ming Huang & Li-Ping Pang & Zun-Quan Xia, 2014. "The space decomposition theory for a class of eigenvalue optimizations," Computational Optimization and Applications, Springer, vol. 58(2), pages 423-454, June.
  70. Hongbo Dong & Min Tao, 2021. "On the Linear Convergence to Weak/Standard d-Stationary Points of DCA-Based Algorithms for Structured Nonsmooth DC Programming," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 190-220, April.
  71. Masao Fukushima & Joaquim Júdice & Welington Oliveira & Valentina Sessa, 2020. "A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem," Computational Optimization and Applications, Springer, vol. 77(3), pages 711-728, December.
  72. N. Dinh & G. Vallet & M. Volle, 2014. "Functional inequalities and theorems of the alternative involving composite functions," Journal of Global Optimization, Springer, vol. 59(4), pages 837-863, August.
  73. Thanh, Phuong Nga & Bostel, Nathalie & Péton, Olivier, 2012. "A DC programming heuristic applied to the logistics network design problem," International Journal of Production Economics, Elsevier, vol. 135(1), pages 94-105.
  74. Hoai Le & Hoai Le Thi & Tao Pham Dinh & Pascal Bouvry, 2010. "A combined DCA: GA for constructing highly nonlinear balanced boolean functions in cryptography," Journal of Global Optimization, Springer, vol. 47(4), pages 597-613, August.
  75. Hoai Le Thi & Tao Pham Dinh & Moulay Belghiti, 2014. "DCA based algorithms for multiple sequence alignment (MSA)," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(3), pages 501-524, September.
  76. Hoai Le & Adnan Yassine & Riadh Moussi, 2012. "DCA for solving the scheduling of lifting vehicle in an automated port container terminal," Computational Management Science, Springer, vol. 9(2), pages 273-286, May.
  77. Weirong Li & Wensheng Zhu, 2024. "Subgroup analysis with concave pairwise fusion penalty for ordinal response," Statistical Papers, Springer, vol. 65(6), pages 3327-3355, August.
  78. Le Thi, H.A. & Pham Dinh, T. & Le, H.M. & Vo, X.T., 2015. "DC approximation approaches for sparse optimization," European Journal of Operational Research, Elsevier, vol. 244(1), pages 26-46.
  79. Xianwen Ding & Jiandong Chen & Xueping Chen, 2020. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 545-568, July.
  80. A. B. Dieker & S. Ghosh & M. S. Squillante, 2017. "Optimal Resource Capacity Management for Stochastic Networks," Operations Research, INFORMS, vol. 65(1), pages 221-241, February.
  81. Welington Oliveira, 2020. "Sequential Difference-of-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 936-959, September.
  82. M. V. Dolgopolik, 2023. "DC semidefinite programming and cone constrained DC optimization II: local search methods," Computational Optimization and Applications, Springer, vol. 85(3), pages 993-1031, July.
  83. A. M. Bagirov & N. Hoseini Monjezi & S. Taheri, 2021. "An augmented subgradient method for minimizing nonsmooth DC functions," Computational Optimization and Applications, Springer, vol. 80(2), pages 411-438, November.
  84. Y. Shi & H. D. Tuan & H. Tuy & S. Su, 2017. "Global optimization for optimal power flow over transmission networks," Journal of Global Optimization, Springer, vol. 69(3), pages 745-760, November.
  85. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
  86. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
  87. N. Dinh & V. Jeyakumar, 2014. "Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 1-22, April.
  88. Ji, Haoran & Wang, Chengshan & Li, Peng & Zhao, Jinli & Song, Guanyu & Wu, Jianzhong, 2018. "Quantified flexibility evaluation of soft open points to improve distributed generator penetration in active distribution networks based on difference-of-convex programming," Applied Energy, Elsevier, vol. 218(C), pages 338-348.
  89. Stefan Sremac & Fei Wang & Henry Wolkowicz & Lucas Pettersson, 2019. "Noisy Euclidean distance matrix completion with a single missing node," Journal of Global Optimization, Springer, vol. 75(4), pages 973-1002, December.
  90. William Haskell & J. Shanthikumar & Z. Shen, 2013. "Optimization with a class of multivariate integral stochastic order constraints," Annals of Operations Research, Springer, vol. 206(1), pages 147-162, July.
  91. Hoai Le Thi & Tao Pham Dinh, 2011. "On solving Linear Complementarity Problems by DC programming and DCA," Computational Optimization and Applications, Springer, vol. 50(3), pages 507-524, December.
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