261
Views
0
CrossRef citations to date
0
Altmetric
Articles

Generalized derivatives of computer programs

&
Pages 480-502 | Received 23 Oct 2019, Accepted 29 Jun 2020, Published online: 26 Jul 2020

References

  • P.I. Barton, K.A. Khan, P. Stechlinski, and H.A.J. Watson, Computationally relevant generalized derivatives: theory, evaluation and applications, Optim. Methods Software. 33 (2018), pp. 1030–1072. doi: 10.1080/10556788.2017.1374385
  • S. Chaudhuri, S. Gulwani, and R. Lublinerman, Continuity analysis of programs, in POPL '10, Madrid, Spain, 2010, pp. 57–70.
  • S. Chaudhuri, S. Gulwani, and R. Lublinerman, Continuity and robustness of programs, Commun. ACM. 55 (2012), pp. 107–115. doi: 10.1145/2240236.2240262
  • S. Chaudhuri and A. Solar-Lezama, Smooth interpretation, in PLDI '10, Vol. 45, Toronto, Ontario, Canada, 2010, p. 279.
  • S. Chaudhuri, S. Gulwani, R. Lublinerman, and S. Navidpour, Proving programs robust, in FSE '11, Szeged, Hungary, 2011, pp. 102–112.
  • F.H. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990.
  • T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, Introduction to Algorithms, MIT Press, Cambridge, MA, 1990.
  • F. Facchinei, A. Fischer, and M. Herrich, An LP-Newton method: Nonsmooth equations, KKT systems, and nonisolated solutions, Math. Program. 146 (2014), pp. 1–36. doi: 10.1007/s10107-013-0676-6
  • A. Griewank, On stable piecewise linearization and generalized algorithmic differentiation, Optim. Methods Software. 28 (2013), pp. 1139–1178. doi: 10.1080/10556788.2013.796683
  • A. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, PA, 2008.
  • D. Hamlet, Continuity in software systems, in ISSTA '02, ACM Press, New York, 2002, pp. 196–200.
  • J.B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms II, Grundlehren der mathematischen Wissenschaften, vol. 306, Springer-Verlag, Berlin, 1993.
  • K. Höffner, K.A. Khan, and P.I. Barton, Generalized derivatives of dynamic systems with a linear program embedded, Automatica 63 (2016), pp. 198–208. http://dx.doi.org/10.1016/j.automatica.2015.10.026
  • S.M. Kakade and J.D. Lee, Provably correct automatic sub-differentiation for qualified programs, in Advances in Neural Information Processing Systems 31, S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, eds., Curran Associates, Inc., 2018, pp. 7125–7135, http://papers.nips.cc/paper/7943-provably-correct-automatic-sub-differentiation-for-qualified-programs.pdf.
  • K.A. Khan, Branch-locking ad techniques for nonsmooth composite functions and nonsmooth implicit functions, Optim. Methods Software 33 (2018), pp. 1127–1155. doi: 10.1080/10556788.2017.1341506
  • K.A. Khan and P.I. Barton, Evaluating an element of the Clarke generalized Jacobian of a composite piecewise differentiable function, ACM Trans. Math. Software 39 (2013), pp. 23:1–23:28. doi: 10.1145/2491491.2491493
  • K.A. Khan and P.I. Barton, A vector forward mode of automatic differentiation for generalized derivative evaluation, Optim. Methods Software 30 (2015), pp. 1185–1212. doi: 10.1080/10556788.2015.1025400
  • K.C. Kiwiel, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics. Springer, Berlin, 1985.
  • M. Mäkelä, Survey of bundle methods for nonsmooth optimization, Optim. Methods Software 17 (2002), pp. 1–29. doi: 10.1080/10556780290027828
  • Y. Nesterov, Lexicographic differentiation of nonsmooth functions, Math. Program. 104 (2005), pp. 669–700. doi: 10.1007/s10107-005-0633-0
  • C.J. Nielsen and P.I. Barton, 110th anniversary: A generalized nonsmooth operator for process integration, Ind. Eng. Chem. Res. 59 (2020), pp. 253–264. doi: 10.1021/acs.iecr.9b02385
  • L. Qi and J. Sun, A nonsmooth version of Newton's method, Math. Program. 58 (1993), pp. 353–367. doi: 10.1007/BF01581275
  • Ž. Sajovic and M. Vuk, Operational calculus on programming spaces (2016), http://arxiv.org/abs/1610.07690.
  • S. Scholtes, Introduction to Piecewise Differentiable Equations, Springer Briefs in Optimization, Springer New York, New York, NY, 2012.
  • N.Z. Shor, Minimization Methods for Non-Differentiable Functions, Springer Series in Computational Mathematics, vol. 3, Springer, Berlin, Heidelberg, 1985.
  • M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2011.
  • H.A.J. Watson, K.A. Khan, and P.I. Barton, Multistream heat exchanger modeling and design, AIChE J. 61 (2015), pp. 3390–3403. doi: 10.1002/aic.14965

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.