Approximating Clarke’s subgradients of semismooth functions by divided differences

1. Bagirov, A.M.: A method for minimizing convex functions based on continuous approximations to the subdifferential. Optim. Methods Softw. 9, 1–17 (1998)

   MATH  MathSciNet  Google Scholar 

2. Chaney, R.W.: Second-order necessary conditions in constrained semismooth optimization. SIAM J. Control Optim. 25, 1072–1081 (1987)

   Article  MATH  MathSciNet  Google Scholar 

3. Chen, X., Nashed, Z., Qi, L.: Smoothing methods and semismooth methods for nondifferentiable operator equations. SIAM J. Numer. Anal. 38, 1200–1216 (2000)

   Article  MATH  MathSciNet  Google Scholar 

4. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley-Interscience, New York (1983)

   MATH  Google Scholar 

5. Hintermüller, M., Hinze, M.: A SQP-semismooth Newton-type algorithm applied to control of the instationary Navier–Stokes system subject to control constraints. SIAM J. Optim. 16, 1177–1200 (2006)

   Article  MATH  MathSciNet  Google Scholar 

6. Hintermüller, M., Kovtunenko, V., Kunish, K.: Semismooth Newton methods for a class of unilaterally constrained variational problems. Adv. Math. Sci. Appl. 14, 513–535 (2004)

   MATH  MathSciNet  Google Scholar 

7. Hintermüller, M., Ulbrich, M.: A mesh-independence result for semismooth Newton methods. Math. Program. 101, 151–184 (2004)

   Article  MATH  MathSciNet  Google Scholar 

8. Facchinei, F., Pang, J.-S.: Finite-dimensional Variational Inequalities and Complementarity Problems, vol 2. Springer, Berlin Heidelberg New York (2003)

   Google Scholar 

9. Mifflin, R.: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control Optim. 15, 959–972 (1977)

   Article  MATH  MathSciNet  Google Scholar 

10. Mifflin, R.: An algorithm for constrained optimization with semismooth functions. Math. Oper. Res. 2, 191–207 (1977)

    MATH  MathSciNet  Google Scholar 

11. Qi, L.: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18, 227–244 (1993)

    Article  MATH  MathSciNet  Google Scholar 

12. Qi, L., Sun, J.: A nonsmooth version of Newton’s method. Math. Program. 58, 353–367 (1993)

    Article  MathSciNet  Google Scholar 

13. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, New Jersey (1970)

    MATH  Google Scholar 

14. Shor, N.Z.: Minimization Methods for Nondifferentiable Functions. Springer, Berlin Heidelberg New York (1985)

    Google Scholar 

15. Studniarski, M.: An algorithm for calculating one subgradient of a convex function of two variables. Numer. Math. 55, 685–693 (1989)

    Article  MATH  MathSciNet  Google Scholar 

16. Śmietański, M.J.: An approximate Newton method for non-smooth equations with finite max functions. Numer. Algorithms 41, 219–238 (2006)

    Article  MathSciNet  MATH  Google Scholar 

17. Ulbrich, M.: Constrained optimal control of Navier–Stokes flow by semismooth Newton methods. Syst. Control. Lett. 48, 297–311 (2003)

    Article  MATH  MathSciNet  Google Scholar 

18. Ulbrich, M.: Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13, 805–842 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references