Skip to main content
SpringerLink
Log in

A Note on Open Problems and Challenges in Optimization Theory and Algorithms

  • Chapter
  • First Online:
Open Problems in Optimization and Data Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 141))

Abstract

In this note, we review some open problems and challenges concerning optimization theory and the algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Agarwal, N., Gonen, A.: Effective dimension of exp-concave optimization (2018). https://arxiv.org/abs/1805.08268

  2. Ahmadi, A.A., Olshevsky, A., Parrilo, P.A., Tsitsiklis, J.N.: NP-hardness of deciding convexity of quartic polynomials and related problems. Math. Program. 137, 453–476 (2013)

    Article  MathSciNet  Google Scholar 

  3. Alabert, A., Berti, A., Caballero, R., Ferrante, M.: No-free-lunch theorem in continuum. Theor. Comput. Sci. 600, 98–106 (2015)

    Article  MathSciNet  Google Scholar 

  4. Allen-Zhu1, Z., Liao, Z., Yuan, Y.: Optimization algorithms for faster computational geometry. In: Chatzigiannakis, I., Mitzenmacher, M., Rabani, Y., Sangiorgi, D. (eds.) 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), Article No. 53, pp. 53:1–53:6. (2016)

    Google Scholar 

  5. Andreatt, M., Bezdek, A., Boronski, J.P.: The problem of Malfatti: two centuries of debate. Math. Intell. 33, 72–76 (2011)

    Article  MathSciNet  Google Scholar 

  6. Battiti, R., Brunato, R., Mascia, F.: Reactive Search and Intelligent Optimization. Operations Research/Computer Science Interfaces Series. Springer, Berlin (2009)

    Google Scholar 

  7. Bennet, C.H., Landauer, R.: The fundamental physical limits of computation. Sci. Am. 253, 48–56 (2014)

    Article  Google Scholar 

  8. Bezdek, K., Deza, A., Ye, Y.: Selected open problems in discrete geometry and optimization. In: Bezdek, K., et al. (eds.) Discrete Geometry and Optimization, pp. 321–336. Springer, Berlin (2013)

    Chapter  Google Scholar 

  9. Cantor, M.: Vorlesungen über Geschichte der Matematik, Band 1. B.G. Teubner, Leipzig (1880)

    Google Scholar 

  10. D’Apuzzo, M., Marino, M., Migdalas, A., Pardalos, P.M., Toraldo, G.: Parallel computing in global optimization. In: Kontoghiorghes, E.J. (ed.) Handbook of Parallel Computing and Statistics, pp. 225–258. Chapman and Hall, Boca Raton (2006)

    Google Scholar 

  11. Euclid’s Elements of Geometry (Edited, and provided with a modern English translation, by Richard Fitzpatrick). http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

  12. Floudas, C.A., Pardalos, P.M. (eds.): Encyclopedia of Optimization, 2nd edn. Springer, Berlin (2009)

    MATH  Google Scholar 

  13. Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126, 43–62 (2001)

    Article  MathSciNet  Google Scholar 

  14. Hedetniemi, S.: Open problems in combinatorial optimization (1998). https://people.cs.clemson.edu/~hedet/preface.html

  15. Hiriart-Urruty, J.-B.: Potpourri of conjectures and open questions in nonlinear analysis and optimization. SIAM Rev. 49, 255–273 (2007)

    Article  MathSciNet  Google Scholar 

  16. Hiriart-Urruty, J.-B.: When only global optimization matters. J. Glob. Optim. 56, 761–763 (2013)

    Article  MathSciNet  Google Scholar 

  17. Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Nonconvex Optimization and Its Applications, vol. 3. Springer, Berlin (2000)

    Google Scholar 

  18. Joyce, T., Herrmann, J.M.: A review of no free lunch theorems, and their implications for metaheuristic optimisation. In: Yang, X.-S. (ed.) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, vol. 744, pp. 27–51. Springer, Berlin (2018)

    Chapter  Google Scholar 

  19. Kore, T.: Open problem: fast stochastic exp-concave optimization. In: JMLR: Workshop and Conference Proceedings, vol. 30, pp. 1–3 (2013)

    Google Scholar 

  20. Markov, I.L.: Limits on fundamental limits to computation. Nature 512, 147–154 (2014)

    Article  Google Scholar 

  21. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge Series on Information and Natural Sciences. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  22. Pardalos, P.M., Rebennack, S.: Computational challenges with cliques, quasi-cliques and clique partitions in graphs. In: Festa, P. (ed.) International Symposium on Experimental Algorithms, SEA 2010: Experimental Algorithms. Lecture Notes in Computer Science, vol. 6049, pp. 13–22. Springer, Berlin (2010)

    Google Scholar 

  23. Pardalos, P.M., Vavasis, S.A.: Open questions in complexity theory for numerical optimization. Math. Programm. 57, 337–339 (1992)

    Article  MathSciNet  Google Scholar 

  24. Serafino, L.: Optimizing without derivatives: what does the no free lunch theorem actually says? Not. AMS 61, 750–755 (2014)

    MathSciNet  MATH  Google Scholar 

  25. Werner, J.: Optimization Theory and Applications. Vieweg Advanced Lectures in Mathematics. Friedr. Vieweg & Son, Braunschweig (1984)

    Google Scholar 

  26. West, D.B.: Open problems - graph theory and combinatorics (2018). https://faculty.math.illinois.edu/~west/openp/

  27. Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  28. Woeginge, G.J.: Open problems around exact algorithms. Discrete Appl. Math. 156, 397–405 (2008)

    Article  MathSciNet  Google Scholar 

  29. Yang, X.-S.: Metaheuristic Optimization: Algorithm Analysis and Open Problems. In: Pardalos, P.M., Rebennack, S. (eds.) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol. 6630. Springer, Berlin (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Industrial Logistics, ETS Institute, Lulea University of Technology, Norrbotten, Sweden

    A. Migdalas

  2. Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Central Macedonia, Greece

    A. Migdalas

  3. Industrial and Systems Engineering Department, University of Florida, Center For Applied Optimization, Gainesville, FL, USA

    P. M. Pardalos

Authors
  1. A. Migdalas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Migdalas .

Editor information

Editors and Affiliations

  1. Industrial and Systems, Engineering Department, University of Florida, Center For Applied Optimization, Gainesville, FL, USA

    Panos M. Pardalos

  2. Industrial Logistics, ETS Institute, Lulea University of Technology, Norrbotten, Sweden

    Athanasios Migdalas

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Migdalas, A., Pardalos, P.M. (2018). A Note on Open Problems and Challenges in Optimization Theory and Algorithms. In: Pardalos, P., Migdalas, A. (eds) Open Problems in Optimization and Data Analysis. Springer Optimization and Its Applications, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-99142-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation