Menu



Exportar registro bibliográfico

Metrics:

Artigo de periodico

A fast gradient and function sampling method for finite-max functions (2018)

  • Authors:
  • Autor USP: HELOU NETO, ELIAS SALOMÃO - ICMC
  • Unidade: ICMC
  • DOI: 10.1007/s10589-018-0030-2
  • Subjects: FUNÇÕES ESPECIAIS; APROXIMAÇÃO; MÉTODOS NUMÉRICOS DE OTIMIZAÇÃO; MÉTODOS ITERATIVOS; OTIMIZAÇÃO MATEMÁTICA; OTIMIZAÇÃO GLOBAL; OTIMIZAÇÃO IRRESTRITA; OTIMIZAÇÃO CONVEXA; OTIMIZAÇÃO ESTOCÁSTICA
  • Keywords: Nonsmooth nonconvex optimization; Gradient sampling; Local superlinear convergence; Global convergence; Unconstrained minimization
  • Agências de fomento:
  • Language: Inglês
  • Imprenta:
  • Source:
    • Acesso à fonteDOI
    Informações sobre o DOI: 10.1007/s10589-018-0030-2 (Fonte: oaDOI API)
    • Este periódico é de assinatura
    • Este artigo é de acesso aberto
    • URL de acesso aberto
    • Cor do Acesso Aberto: green
    How to cite
    A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas

    • ABNT

      HELOU NETO, Elias Salomão; SANTOS, Sandra A.; SIMÕES, Lucas E. A. A fast gradient and function sampling method for finite-max functions. Computational Optimization and Applications, Berlin, Heidelberg, Springer Nature, v. 71, n. 3, p. 673-717, 2018. Disponível em: < http://dx.doi.org/10.1007/s10589-018-0030-2 > DOI: 10.1007/s10589-018-0030-2.

    • APA

      Helou Neto, E. S., Santos, S. A., & Simões, L. E. A. (2018). A fast gradient and function sampling method for finite-max functions. Computational Optimization and Applications, 71( 3), 673-717. doi:10.1007/s10589-018-0030-2

    • NLM

      Helou Neto ES, Santos SA, Simões LEA. A fast gradient and function sampling method for finite-max functions [Internet]. Computational Optimization and Applications. 2018 ; 71( 3): 673-717.Available from: http://dx.doi.org/10.1007/s10589-018-0030-2

    • Vancouver

      Helou Neto ES, Santos SA, Simões LEA. A fast gradient and function sampling method for finite-max functions [Internet]. Computational Optimization and Applications. 2018 ; 71( 3): 673-717.Available from: http://dx.doi.org/10.1007/s10589-018-0030-2

    Referências citadas na obra
    Balinski, M.L., Wolfe, P.: Nondifferentiable Optimization. Mathematical Programming Studies, vol. 3. North-Holland, Amsterdam (1975)
    Bonnans, J.F., Gilbert, J.C., Lemaréchal, C., Sagastizábal, C.A.: Numerical Optimization: Theoretical and Practical Aspects, 2nd edn. Springer, Berlin (2006)
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
    Burke, J.V., Lewis, A.S., Overton, M.L.: Approximating subdifferentials by random sampling of gradients. Math. Oper. Res. 27(3), 567–584 (2002)
    Burke, J.V., Lewis, A.S., Overton, M.L.: A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM J. Optim. 15(3), 751–779 (2005)
    Clarke, F.H.: Optimization and Nonsmooth Analysis, vol. 5. SIAM, Montreal (1990)
    Clarke, F.H., Ledyaev, Y.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory, vol. 178. Springer, New York (2008)
    Crema, A., Loreto, M., Raydan, M.: Spectral projected subgradient with a momentum term for the Lagrangean dual approach. Comput. Oper. Res. 34(10), 3174–3186 (2007)
    Curtis, F.E., Overton, M.L.: A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization. SIAM J. Optim. 22(2), 474–500 (2012)
    Curtis, F.E., Que, X.: An adaptive gradient sampling algorithm for non-smooth optimization. Optim. Methods Softw. 28(6), 1302–1324 (2013)
    Curtis, F.E., Que, X.: A quasi-Newton algorithm for nonconvex, nonsmooth optimization with global convergence guarantees. Math. Program. Comput. 7(4), 399–428 (2015)
    Daniilidis, A., Sagastizábal, C., Solodov, M.: Identifying structure of nonsmooth convex functions by the bundle technique. SIAM J. Optim. 20(2), 820–840 (2009)
    Di Pillo, G., Grippo, L., Lucidi, S.: A smooth method for the finite minimax problem. Math. Program. 60(1), 187–214 (1993)
    Do, T.M.T., Artières, T.: Regularized bundle methods for convex and non-convex risks. J. Mach. Learn. Res. 13(1), 3539–3583 (2012)
    Dotta, D., Silva, A.S., Decker, I.C.: Design of power system controllers by nonsmooth, nonconvex optimization. In: Power Energy Society General Meeting, 2009. PES ’09. IEEE, pp. 1–7 (2009)
    Du, D.Z., Pardalos, P.M.: Minimax and Applications, vol. 4. Springer, Boston (2013)
    Fuduli, A., Gaudioso, M., Giallombardo, G.: A DC piecewise affine model and a bundling technique in nonconvex nonsmooth minimization. Optim. Methods Softw. 19(1), 89–102 (2004)
    Gaudioso, M., Gorgone, E., Monaco, M.F.: Piecewise linear approximations in nonconvex nonsmooth optimization. Numerische Mathematik 113(1), 73–88 (2009)
    Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 47(1), 99–131 (2005)
    Goldstein, A.A.: Optimization of Lipschitz continuous functions. Math. Program. 13(1), 14–22 (1977)
    Griewank, A., Walther, A.: Evaluating Derivatives, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2008)
    Grothey, A., McKinnon, K.: A superlinearly convergent trust region bundle method. Report, Department of Mathematics & Statistics, Edinburgh University (1998)
    Haarala, M., Miettinen, K., Mäkelä, M.M.: New limited memory bundle method for large-scale nonsmooth optimization. Optim. Methods Softw. 19(6), 673–692 (2004)
    Helou, E.S., Santos, S.A., Simões, L.E.A.: On the differentiability check in gradient sampling methods. Optim. Methods Softw. 31(5), 983–1007 (2016)
    Helou, E.S., Santos, S.A., Simões, L.E.A.: On the local convergence analysis of the gradient sampling method for finite max-functions. J. Optim. Theory Appl. 175(1), 137–157 (2017)
    Hiriart-Urruty, J.B., Lemaréchal, C.: Convex Analysis and Minimization Algorithms I. Springer, New York (1993)
    Huber, G.: Gamma function derivation of n-sphere volumes. Am. Math. Mon. 89(5), 301–302 (1982)
    Kelley Jr., J.E.: The cutting-plane method for solving convex programs. J. Soc. Ind. Appl. Math. 8(4), 703–712 (1960)
    Kiwiel, K.C.: Methods of descent for nondifferentiable optimization, vol. 1133. Springer, Berlin (1985)
    Kiwiel, K.C.: Restricted step and Levenberg–Marquardt techniques in proximal bundle methods for nonconvex nondifferentiable optimization. SIAM J. Optim. 6(1), 227–249 (1996)
    Kiwiel, K.C.: Convergence of the gradient sampling algorithm for nonsmooth nonconvex optimization. SIAM J. Optim. 18(2), 379–388 (2007)
    Lemaréchal, C., Mifflin, R.: Global and superlinear convergence of an algorithm for one-dimensional minimization of convex functions. Math. Program. 24(1), 241–256 (1982)
    Lemaréchal, C., Oustry, F., Sagastizábal, C.: The U-Lagrangian of a convex function. Trans. Am. Math. Soc. 352(2), 711–729 (2000)
    Lemaréchal, C., Sagastizábal, C.: Practical aspects of the moreau–yosida regularization: theoretical preliminaries. SIAM J. Optim. 7(2), 367–385 (1997)
    Lewis, A.S.: Active sets, nonsmoothness, and sensitivity. SIAM J. Optim. 13(3), 702–725 (2002)
    Lewis, A.S., Overton, M.L.: Nonsmooth optimization via quasi-Newton methods. Math. Program. 141(1–2), 135–163 (2013)
    Loreto, M., Aponte, H., Cores, D., Raydan, M.: Nonsmooth spectral gradient methods for unconstrained optimization. EURO J. Comput. Optim. 5(4), 529–553 (2017)
    Lukšan, L., Vlček, J.: A bundle-Newton method for nonsmooth unconstrained minimization. Math. Program. 83(1–3), 373–391 (1998)
    Mäkelä, M.: Survey of bundle methods for nonsmooth optimization. Optim. Methods Softw. 17(1), 1–29 (2002)
    Maratos, N.: Exact penalty function algorithms for finite dimensional and control optimization problems. Ph.D. thesis, Imperial College, London (1978)
    Maréchal, P., Ye, J.J.: Optimizing condition numbers. SIAM J. Optim. 20(2), 935–947 (2009)
    Mifflin, R., Sagastizábal, C.: VU-decomposition derivatives for convex max-functions. In: Théra, M., Tichatschke, R. (eds.) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol. 477, pp. 167–186. Springer, Berlin (1999)
    Mifflin, R., Sagastizábal, C.: A VU-algorithm for convex minimization. Math. Program. 104(2–3), 583–608 (2005)
    Mifflin, R., Sagastizábal, C.: A science fiction story in nonsmooth optimization originating at IIASA. In: Grötschel, M. (ed.) Documenta Mathematica Optimization Stories, pp. 291–300. Deutschen Mathematiker-Vereinigung, Bielefeld (2012)
    Miller, S.A., Malick, J.: Newton methods for nonsmooth convex minimization: connections among $$\cal{U}$$ U -Lagrangian, Riemannian Newton and SQP methods. Math. Program. 104(2), 609–633 (2005)
    Moreau, J.J., Panagiotopoulos, P.D.: Nonsmooth Mechanics and Applications, vol. 302. Springer, Vienna (2014)
    Nocedal, J., Wright, S.: Numerical Optimization, 2nd edn. Springer, New York (2006)
    Oliveira, W., Sagastizábal, C.: Bundle methods in the XXIst century: a bird’s-eye view. Pesquisa Operacional 34(3), 647–670 (2014)
    Outrata, J., Kočvara, M., Zowe, J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results, vol. 28. Kluwer Academic Publishers, The Netherlands (2013)
    Peng, C., Jin, X., Shi, M.: Epidemic threshold and immunization on generalized networks. Phys. A Stat. Mech. Appl. 389(3), 549–560 (2010)
    Wang, F.C., Chen, H.T.: Design and implementation of fixed-order robust controllers for a proton exchange membrane fuel cell system. Int. J. Hydrog. Energy 34(6), 2705–2717 (2009)
    Zhang, J., Kim, N.H., Lasdon, L.: An improved successive linear programming algorithm. Manag. Sci. 31(10), 1312–1331 (1985)
    Últimas obras dos mesmos autores vinculados com a USP cadastradas na BDPI:

AGUIA

Digital Library of Intellectual Production of Universidade de São Paulo     2012 - 2020