The Recession Function of Convex Functions and Its Applications

wen huang

Article ID: 10075
Vol 8, Issue 2, 2025

VIEWS - 17 (Abstract)

Abstract


The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.


Keywords


recession cone; recession function; lower unboundness; positive homogeneity



References

  1. R. T. Rockafellar. Convex Analysis[M]. Princeton University Press, 1979.
  2. D. P. Bertsekas. Convex Optimization Theory[M]. Athena Scientific, 2009.
  3. W. T. Obuchowska, K. G. Murty. Cone of recession and unboundedness of convex functions[J]. European Journal of
  4. Operational Research, 2001, 133(02): 409-415.
  5. W. T. Obuchowska. On the Minimizing Trajectory of Convex Functions with Unbounded Level Sets[J]. Computational
  6. Optimization and Applications, 2004, 27: 37-52.
  7. A. Auslender. How to deal with the unbounded in optimization: Theory and algorithms[J]. Mathematical Programming, 1997, 79: 3-18.
  8. G. Beer. Recession cones of nonconvex sets and increase functions[J]. Proceedings of the American Mathematical Society, 1979, 73(2): 228--232.
  9. Robert, A. Abrams. Technical note—optimality conditions and recession cones[J]. Operations Research, 1975, 23(3): 549--553.
  10. R. T. Rockafellar, R. J. B. Wets. Variational Analysis[M]. Springer, 2004
  11. A. Auslender, M. Teboulle. Asymptotic Cones and Functions In Optimization and Variational Inequalities[M]. Springer, 2003.
  12. F. Lara. Generalized asymptotic functions in nonconvex multiobjective optimization problems[J]. Optimization, 2017, 66: 1259--1272.
  13. Genghua Li, Shengjie Li, Manxue You. Recession function and its applications in optimization[J]. Optimization, 2021, 70: 2559--2578.
  14. Genghua Li, Shengjie Li, Manxue You. Asymptotic analysis of scalarization functions and applications[J]. Journal of Industrial and Management Optimization, 2023, 19(4): 2367--2380.


DOI: https://doi.org/10.24294/ijmss10075

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Creative Commons License

This site is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.