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Two “Well-Known” Properties of Subgradient Optimization

Bibliographic reference Wolsey, Laurence ; Anstreicher, Kurt. Two “Well-Known” Properties of Subgradient Optimization. In: Mathematical Programming Journal, Vol. 120, no. 1, p. 213-220 (2009)
Permanent URL http://hdl.handle.net/2078/18073
  1. Anstreicher, K.M., Wolsey, L.A.: On dual solutions in subgradient optimization. Center for Operations Research and Econometrics. Louvain-la-Neuve, Belgium (1992, working paper)
  2. Bahiense L., Maculan N., Sagastizábal C. (2002). The volume algorithm revisited: relation with bundle methods. Math. Program. 94: 41–69
  3. Barahona F., Anbil R. (2000). The volume algorithm: producing primal solutions with a subgradient method. Math. Program. 87: 385–399
  4. Barahona F., Anbil R. (2002). On some difficult linear programs coming from set partitioning. Discret. Appl. Math. 118: 3–11
  5. Correa R., Lemaréchal C. (1993). Convergence of some algorithms for convex minimization. Math. Program. 62: 261–275
  6. Dubost L., Gonzalez R., Lemaréchal C. (2005). A primal-proximal heuristic applied to the French unit-commitment problem. Math. Program. 104: 129–151
  7. Ermol’ev Yu. (1976). Methods of stochastic programming. Nauka, Moscow
  8. Goffin J.L. (1977). On the convergence rates of subgradient optimization methods. Math. Program. 13: 329–347
  9. Held M., Wolfe P., Crowder H. (1974). Validation of subgradient optimization. Math. Program. 6: 62–88
  10. Larsson T., Liu Z. (1997). A Lagrangian relaxation scheme for structured linear programs with application to multicommodity network flow. Optimization 40: 247–284
  11. Larsson T., Patriksson M., Strömberg A.-B. (1996). Conditional subgradient optimization—theory and applications. Eur. J. Oper. Res. 88: 382–403
  12. Larsson T., Patriksson M., Strömberg A.-B. (1998). Ergodic convergence in subgradient optimization. Optim. Methods Softw. 9: 93–120
  13. Larsson T., Patriksson M., Strömberg A.-B. (1999). Ergodic, primal convergence in dual subgradient schemes for convex programming. Math. Program. 86: 283–312
  14. Lemaréchal C.: (2001). Lagrangian relaxation. In: Jünger, M., Nadef, D. (eds) Computational Combinatorial Optimization, pp 112–156. Springer, Heidelberg
  15. Nemirovskii, A.: Private communication (1993)
  16. Polyak B.T. (1967). A general method for solving extremum problems. Soviet Math Doklady 8: 593–597
  17. Polyak B.T. (1977). Subgradient methods: a survey of Soviet research. In: Lemaréchal, C.L., Mifflin, R. (eds) Nonsmooth Optimization, Proceedings of a IIASA Workshop, March 28–April 8, 1977. Pergamon Press, New York
  18. Polyak B.T. (1987). Introduction to Optimization. Optimization Software, Inc., New York
  19. Rudin W. (1976). Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York
  20. Shepilov M.A. (1976). Method of the generalized gradient for finding the absolute minimum of a convex function. Cybernetics 12: 547–553
  21. Sherali H.D., Choi G. (1996). Recovery of primal solutions when using subgradient optimization methods to solve Lagrangian duals of linear programs. Oper. Res. Lett. 19: 105–113
  22. Shor Naum Zuselevich, Minimization Methods for Non-Differentiable Functions, ISBN:9783642821202, 10.1007/978-3-642-82118-9