Subgradient Methods for Saddle-Point Problems
Tóm tắt
Từ khóa
Tài liệu tham khảo
Low, S., Lapsley, D.E.: Optimization flow control, I: Basic algorithm and convergence. IEEE/ACM Trans. Netw. 7(6), 861–874 (1999)
Chiang, M., Low, S.H., Calderbank, A.R., Doyle, J.C.: Layering as optimization decomposition: a mathematical theory of network architectures. Proc. IEEE 95(1), 255–312 (2007)
Arrow, K.J., Hurwicz, L., Uzawa, H.: Studies in Linear and Non-Linear Programming. Stanford University Press, Stanford (1958)
Bruck, R.E.: On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space. J. Math. Anal. Appl. 61, 159–164 (1977)
Nemirovski, A.S., Judin, D.B.: Cezare convergence of gradient method approximation of saddle points for convex-concave functions. Dokl. Akad. Nauk SSSR 239, 1056–1059 (1978)
Uzawa, H.: Iterative methods in concave programming. In: Arrow, K., Hurwicz, L., Uzawa, H. (eds.) Studies in Linear and Nonlinear Programming, pp. 154–165. Stanford University Press, Stanford (1958)
Gol’shtein, E.G.: A generalized gradient method for finding saddle points. Matekon 10, 36–52 (1974)
Maistroskii, D.: Gradient methods for finding saddle points. Matekon 13, 3–22 (1977)
Zabotin, I.Y.: A subgradient method for finding a saddle point of a convex-concave function. Issled. Prikl. Mat. 15, 6–12 (1988)
Korpelevich, G.M.: The extragradient method for finding saddle points and other problems. Matekon 13, 35–49 (1977)
Kallio, M., Ruszczyński, A.: Perturbation methods for saddle point computation. Report No. WP-94-38, International Institute for Applied Systems Analysis (1994)
Kallio, M., Rosa, C.H.: Large-scale convex optimization via saddle-point computation. Oper. Res. 47, 93–101 (1999)
Beck, A., Teboulle, M.: Mirror descent and nonlinear projected subgradient methods for convex optimization. Oper. Res. Lett. 31, 167–175 (2003)
Nemirovski, A.S.: Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1), 229–251 (2004)
Auslender, A., Teboulle, M.: Interior gradient and proximal methods for convex and conic optimization. SIAM J. Optim. 16, 697–725 (2006)
Auslender, A., Teboulle, M.: Projected subgradient methods with non-Euclidean distances for nondifferentiable convex minimization and variational inequalities. Math. Program., Ser. B (2007). doi: 10.1007/s10107-007-0147-z
Shor, N.Z.: Minimization methods for Nondifferentiable Functions. Springer, Berlin (1985). Translated from Russian by K.C. Kiwiel and A. Ruszczynski
Polyak, B.T.: Introduction to Optimisation. Optimization Software, New York (1987)
Demyanov, V.F., Vasilyev, L.V.: Nondifferentiable Optimization. Optimization Software, New York (1985)
Correa, R., Lemaréchal, C.: Convergence of some algorithms for convex minimization. Math. Program. 62, 261–271 (1993)
Nedić, A., Bertsekas, D.P.: Convergence rate of incremental subgradient algorithms. In: Uryasev, S., Pardalos, P. (eds.) Stochastic Optimization: Algorithms and Applications. Kluwer Academic, Dordrecht (2000)
Nedić, A., Bertsekas, D.P.: Incremental subgradient methods for nondifferentiable optimization. SIAM J. Optim. 12(1), 109–138 (2001)
Nedić, A., Ozdaglar, A.: Approximate primal solutions and rate analysis for dual subgradient methods. SIAM J. Optim. 19, 1757–1780 (2009)
Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Cambridge (1999)
Bertsekas, D.P., Nedić, A., Ozdaglar, A.: Convex Analysis and Optimization. Athena Scientific, Belmont (2003)
Sherali, H.D., Choi, G.: Recovery of primal solutions when using subgradient optimization methods to solve Lagrangian duals of linear programs. Oper. Res. Lett. 19, 105–113 (1996)
Larsson, T., Patriksson, M., Strömberg, A.: Ergodic results and bounds on the optimal value in subgradient optimization. In: Kelinschmidt, P., (eds.) Operations Research Proceedings, pp. 30–35. Springer, Berlin (1995)
Larsson, T., Patriksson, M., Strömberg, A.: Ergodic convergence in subgradient optimization. Optim. Methods Soft. 9, 93–120 (1998)
Larsson, T., Patriksson, M., Strömberg, A.: Ergodic primal convergence in dual subgradient schemes for convex programming. Math. Program. 86, 283–312 (1999)
Nesterov, Y.: Primal-dual subgradient methods for convex problems. Center for Operations Research and Econometrics (CORE) Report No. 67, Catholic University of Louvain (UCL) (2005)
Hiriart-Urruty, J.-B., Lemaréchal, C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1996)