References
- El Ghali A, El Moudden M. An implementation of a reduced subgradient method via Luenberger– Mokhtar variant. Optimization. 2016;65(7):1497–1518. doi: https://doi.org/10.1080/02331934.2016.1147037
- Demyanov VF, Stavroulakis GE, Polyakova LN, et al. Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics, nonconvex optimization and its applications. Vol. 10. Dordrecht: Springer; 1996.
- Bagirov A, Karmitsa N, Mäkelä MM. Introduction to nonsmooth optimization: theory, practice and software. Switzerland: Springer; 2014.
- Shor N. Minimization methods for non-differentiable functions. Berlin: Springer-Verlag; 1985.
- Kappel F, Kuntsevich AV. An implementation of Shor's r-algorithm. Comput Optim Appl. 2000;15(2):193–205. doi: https://doi.org/10.1023/A:1008739111712
- Hiriart-Urruty JB, Lemaréchal C. Convex analysis and minimization algorithms
. Berlin: Springer-Verlag; 1993.
- Kiwiel KC. Methods of descent for nondifferentiable optimization. Berlin: Springer; 1985. (Lecture notes in mathematics; 1133).
- Burke JV, Lewis AS, Overton ML. A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM J Optim. 2005;15(3):751–779. doi: https://doi.org/10.1137/030601296
- Curtis FE, Overton ML. A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization. SIAM J Optim. 2012;22(2):474–500. doi: https://doi.org/10.1137/090780201
- Lemaréchal C. An extension of Davidon methods to non differentiable problems. Math Programming Study. 1975;3:95–109. doi: https://doi.org/10.1007/BFb0120700
- Wolfe P. A method of conjugate subgradients for minimizing nondifferentiable functions. Math Programming Study. 1975;3:145–173. doi: https://doi.org/10.1007/BFb0120703
- Feltenmark S, Kiwiel KC. Dual applications of proximal bundle methods, including Lagrangian relaxation of nonconvex problems. SIAM J Optim. 2000;10(3):697–721. doi: https://doi.org/10.1137/S1052623498332336
- Mäkelä MM. Multiobjective proximal bundle method for nonconvex nonsmooth optimization: Fortran subroutine MPBNGC 2.0. Rep Dept Math Inform Technol B Sci Comput. 2003;13:2003.
- Yang Y, Pang L, Ma X, et al. Constrained nonconvex nonsmooth optimization via proximal bundle method. J Optim Theory Appl. 2014;163(3):900–925. doi: https://doi.org/10.1007/s10957-014-0523-9
- Fuduli A, Gaudioso M, Nurminski E. A splitting bundle approach for non-smooth non-convex minimization. Optimization. 2015;64(5):1131–1151. doi: https://doi.org/10.1080/02331934.2013.840625
- Dempe S, Bard JF. Bundle trust-region algorithm for bilinear bilevel programming. J Optim Theory Appl. 2001;110(2):265–288. doi: https://doi.org/10.1023/A:1017571111854
- Apkarian P, Noll D, Ravanbod L. Nonsmooth bundle trust-region algorithm with applications to robust stability. Set-Valued Var Anal. 2016;24(1):115–148. doi: https://doi.org/10.1007/s11228-015-0352-5
- Hare W, Sagastizábal C. A redistributed proximal bundle method for nonconvex optimization. SIAM J Optim. 2010;20(5):2442–2473. doi: https://doi.org/10.1137/090754595
- Hare W, Sagastizábal C, Solodov M. A proximal bundle method for nonsmooth nonconvex functions with inexact information. Comput Optim Appl. 2016;63(1):1–28. doi: https://doi.org/10.1007/s10589-015-9762-4
- Lv J, Pang LP, Meng FY. A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information. J Global Optim. 2018;70(3):517–549. doi: https://doi.org/10.1007/s10898-017-0565-2
- Mäkelä M. Survey of bundle methods for nonsmooth optimization. Optim Methods Sof. 2002;17(1):1–29. doi: https://doi.org/10.1080/10556780290027828
- Kuntsevich A, Kappel F. Solvopt-the solver for local nonlinear optimization problems: Matlab, c and FORTRAN source codes. Institute for Mathematics, Karl-Franzens University of Graz; 1997.
- Wolfe P. The reduced gradient method. Santa Monica: Rand Document; 1962.
- Huard P. Un algorithme général de gradient réduit. Bulletin De La Direction Des Etudes Et Recherches, EDF, Série C. 1982;2:91-–109.
- Mokhtar-Kharroubi H. Sur quelques méthodes de gradient réduit sous contraintes linéaires. RAIRO-Analyse Numerique. 1979;13(2):167–180. doi: https://doi.org/10.1051/m2an/1979130201671
- Chi-Ye M Yeuh. A new reduced gradient method. Sci Sin. 1979;22:1099-–1113.
- El Mouatasim A, Ellaia R, de Cursi ES. Stochastic perturbation of reduced gradient & GRG methods for nonconvex programming problems. Appl Math Comput. 2014;226:198-–211.
- El Mouatasim A. Implementation of reduced gradient with bisection algorithms for non-convex optimization problem via stochastic perturbation. Numer Algorithms. 2018;78(1):41–62. doi: https://doi.org/10.1007/s11075-017-0366-1
- Gochet W, Smeers Y. A modified reduced gradient method for a class of nondifferentiable problems. Math Program. 1980;19:137–154. doi: https://doi.org/10.1007/BF01581637
- Bihain A, Nguyen VH, Strodiot JJ. A reduced subgradient algorithm. Math Program Study. 1987;30:127–149. doi: https://doi.org/10.1007/BFb0121158
- Strodiot JJ, Nguyen VH, Heukemes N. ϵ-optimal solutions in nondifferentiable convex programming and some related questions. Math Program. 1983;25(3):307–328. doi: https://doi.org/10.1007/BF02594782
- Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
- Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1990, reprinted by New York: SIAM; 1983.
- Lemaréchal C, Strodiot JJ, Bihain A. On a bundle algorithm for nonsmooth optimization. In Managasarin OL, Meyer RR and SM Robinson, editors. Nonlinear programming. Vol. 4. New York (NY): Academic Press; 1981. p. 245–281.
- Mifflin R. A modification and an extension of Lemaréchal's algorithm for nonsmooth minimization. Math Program Study. 1982;17:77–90. doi: https://doi.org/10.1007/BFb0120960
- Bihain A. Numerical and algorithmic contributions to the constrained optimization of some classes of non-differentiable functions [dissertation]. Namur, Belgium: Facultés Universitaires Notre-Dame de la Paix; 1984.
- Luenberger DG, Ye Y. Linear and nonlinear programming. New York, USA: Springer Science & Business Media; 2008.
- Lemaréchal C. A view of line searches. In Auslender A, Oettli W and Stoer J, editors. Lecture notes in control and information science. Berlin: Springer; 1981.
- Madsen K, Schjaer-Jacobsen H. Linearly constrained minimax optimization. Math Program. 1978;14(1):208–223. doi: https://doi.org/10.1007/BF01588966
- Kiwiel KC. Proximity control in bundle methods for convex nondifferentiable minimization. Math Program. 1990;46:105–122. doi: https://doi.org/10.1007/BF01585731
- Lukšan L, Vlcek J. Test problems for nonsmooth unconstrained and linearly constrained optimization. Institute of Computer Science, Academy of Sciences of the Czech Republic; No. 798. 2000.
- Bagirov AM, Ghosh M, Webb D. A derivative-free method for linearly constrained nonsmooth optimization. J Indust Manage Optim. 2006;2(3):319.