A DC approach for minimax fractional optimization programs with ratios of convex functions

References

• S. Addoune, K. Boufi, and A. Roubi, Proximal bundle algorithms for nonlinearly constrained convex minimax fractional programs, J. Optim. Theory Appl. 179 (2018), pp. 212–239. doi: 10.1007/s10957-018-1342-1
   Web of Science ®Google Scholar
• S. Addoune, M. El Haffari, and A. Roubi, A proximal point algorithm for generalized fractional programs, Optim. 66(9) (2017), pp. 1495–1517. doi: 10.1080/02331934.2017.1338698
   Web of Science ®Google Scholar
• A. Bagirov, N. Karmitsa, and M.M. Mäkelä, Introduction to Nonsmooth Optimization: Theory, Practice and Software, Springer, Cham, 2014.
   Google Scholar
• A.I. Barros, J.B.G. Frenk, S. Schaible, and S. Zhang, A new algorithm for generalized fractional programs, Math. Program. 72 (1996), pp. 147–175.
   Web of Science ®Google Scholar
• A.I. Barros, J.B.G. Frenk, S. Schaible, and S. Zhang, Using duality to solve generalized fractional programming problems, J. Glob. Optim. 8 (1996), pp. 139–170. doi: 10.1007/BF00138690
   Web of Science ®Google Scholar
• C.R. Bector, S. Chandra, and M.K. Bector, Generalized fractional programming duality: a parametric approach, J. Optim. Theory Appl. 60(2) (1989), pp. 243–260. doi: 10.1007/BF00940006
   Web of Science ®Google Scholar
• J.C. Bernard and J.A. Ferland, Convergence of interval-type algorithms for generalized fractional programming, Math. Program. 43 (1989), pp. 349–363. doi: 10.1007/BF01582298
   Web of Science ®Google Scholar
• H. Boualam and A. Roubi, Dual algorithms based on the proximal bundle method for solving convex minimax fractional programs, J. Ind. Manag. Optim. 15(4) (2019), pp. 1897–1920.
   Google Scholar
• H. Boualam and A. Roubi, Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs, J. Global Optim. 74(2) (2019), pp. 255–284. doi: 10.1007/s10898-019-00757-2
   Web of Science ®Google Scholar
• K. Boufi and A. Roubi, Dual method of centers for solving generalized fractional programs, J. Glob. Optim. 69(2) (2017), pp. 387–426. doi: 10.1007/s10898-017-0523-z
   Web of Science ®Google Scholar
• K. Boufi and A. Roubi, Duality results and dual bundle methods based on the dual method of centers for minimax fractional programs, SIAM J. Optim. 29(2) (2019), pp. 1578–1602. doi: 10.1137/18M1199708
   Web of Science ®Google Scholar
• K. Boufi and A. Roubi, Prox-regularization of the dual method of centers for generalized fractional programs, Optim. Methods Softw. 34(3) (2019), pp. 515–545. doi: 10.1080/10556788.2017.1392520
   Web of Science ®Google Scholar
• F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
   Google Scholar
• J-P. Crouzeix and J.A. Ferland, Algorithms for generalized fractional programming, Math. Program. 52 (1991), pp. 191–207. doi: 10.1007/BF01582887
   Web of Science ®Google Scholar
• J-P. Crouzeix, J.A. Ferland, and H.V. Nguyen, Revisiting Dinkelbach-type algorithms for generalized fractional programs, OPSEARCH 45 (2008), pp. 97–110. doi: 10.1007/BF03398807
   Google Scholar
• J-P. Crouzeix, J.A. Ferland, and S. Schaible, Duality in generalized linear fractional programming, Math. Program. 27 (1983), pp. 342–354. doi: 10.1007/BF02591908
   Web of Science ®Google Scholar
• J-P. Crouzeix, J.A. Ferland, and S. Schaible, An algorithm for generalized fractional programs, J. Optim. Theory Appl. 47 (1985), pp. 35–49. doi: 10.1007/BF00941314
   Web of Science ®Google Scholar
• J-P. Crouzeix, J.A. Ferland, and S. Schaible, A note on an algorithm for generalized fractional programs, J. Optim. Theory Appl. 50 (1986), pp. 183–187. doi: 10.1007/BF00938484
   Web of Science ®Google Scholar
• M. El Haffari and A. Roubi, Convergence of a proximal algorithm for solving the dual of a generalized fractional program, RAIRO-Oper. Res. 51(4) (2017), pp. 985–1004. doi: 10.1051/ro/2017004
   Web of Science ®Google Scholar
• M. El Haffari and A. Roubi, Prox-dual regularization algorithm for generalized fractional programs, J. Ind. Manag. Optim. 13(4) (2017), pp. 1991–2013.
   Google Scholar
• J-B. Hiriart-Urruty, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions, in Convexity and Duality in Optimization, J. Ponstein, ed., Springer, Berlin, 1985, Vol. 256, pp. 37–70.
   Google Scholar
• J-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I, Springer, Berlin, 1993.
   Google Scholar
• R. Jagannathan and S. Schaible, Duality in generalized fractional programming via Farkas' lemma, J. Optim. Theory Appl. 41(3) (1983), pp. 417–424. doi: 10.1007/BF00935361
   Web of Science ®Google Scholar
• T. Pham Dinh and S. El Bernoussi, Algorithms for solving a class of nonconvex optimization problems. Methods of subgradients, Vol. 129, Fermat days 85, Mathematics for Optimization, North-Holland Mathematics Studies, North-Holland, Amsterdam, 1986.
   Google Scholar
• A. Roubi, Method of centers for generalized fractional programming, J. Optim. Theory Appl. 107(1) (2000), pp. 123–143. doi: 10.1023/A:1004660917684
   Web of Science ®Google Scholar
• A. Roubi, Convergence of prox-regularization methods for generalized fractional programming, RAIRO Oper. Res. 36(1) (2002), pp. 73–94. doi: 10.1051/ro:2002006
   Web of Science ®Google Scholar
• I.M. Stancu-Minasian, A sixth bibliography of fractional programming, Optimization 55 (2006), pp. 405–428. doi: 10.1080/02331930600819613
   Web of Science ®Google Scholar
• I.M. Stancu-Minasian, A seventh bibliography of fractional programming, Adv. Model. Optim. 15 (2013), pp. 309–386.
   Google Scholar
• I.M. Stancu-Minasian, A eighth bibliography of fractional programming, Optimization 66 (2017), pp. 439–470. doi: 10.1080/02331934.2016.1276179
   Web of Science ®Google Scholar
• J.-J. Strodiot, J.-P. Crouzeix, J.A. Ferland, and V.H. Nguyen, An inexact proximal point method for solving generalized fractional programs, J. Glob. Optim. 42(1) (2008), pp. 121–138. doi: 10.1007/s10898-007-9270-x
   Web of Science ®Google Scholar
• H.A. Le Thi and T. Pham Dinh, The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems, Ann. Oper. Res. 133 (2005), pp. 23–46. doi: 10.1007/s10479-004-5022-1
   Web of Science ®Google Scholar
• H.A. Le Thi and T. Pham Dinh, DC programming and DCA: thirty years of developments, Math. Program. Ser. B 15 (2015), pp. 137–161.
   Google Scholar