We study marginal functions of functions defined on arbitrary subsets of Rn\mathbb{R}^n, especially the convexity properties which such functions can possess.

Contact details are reproduced from the original publication and may be historical.

Christer Oscar Kiselman

Department of Information Technology, Uppsala University, Sweden

kiselman@it.uu.se
  1. M. Andramonov, A. Ellero: Generalised convexity properties of marginal functions, in: Progress in Optimization, A. Eberhard et al. (eds.), Applied Optimization vol. 30, Kluwer, Dordrecht (1999) 59–78.https://doi.org/10.1007/978-1-4613-3285-5_3Google Scholar
  2. A. V. Fiacco, J. Kyparisis: Convexity and concavity properties of the optimal value function in parametric nonlinear programming, J. Optim. Theory Appl. 48/1 (1986) 95–126.https://doi.org/10.1007/BF00938592Google Scholar
  3. J.-B. Hiriart-Urruty, C. Lemaréchal: Fundamentals of Convex Analysis, Springer, Berlin (2001).https://doi.org/10.1007/978-3-642-56468-0Google Scholar
  4. C. O. Kiselman: Duality of convolution operators. A tool for shape analysis, Mathematics and Visualization, Springer, Berlin (2021), to appear.Google Scholar
  5. C. O. Kiselman: Elements of Digital Geometry, Mathematical Morphology, and Discrete Optimization, World Scientific, Singapore (2022).https://doi.org/10.1142/12584Google Scholar
  6. C. O. Kiselman, S. Samieinia: Convexity of marginal functions in the discrete case, in: Digital Geometry, Combinatorics, and Discrete Optimization, S. Samieinia, PhD Thesis, Stockholm University (2010).Google Scholar
  7. C. O. Kiselman, S. Samieinia: Convexity of marginal functions in the discrete case, in: Analysis Meets Geometry. The Mikael Passare Memorial Volume, M. Anderson et al. (eds.), Birkhäuser, Cham (2017) 287–309.https://doi.org/10.1007/978-3-319-52471-9_18Google Scholar
  8. R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton (1970, 1979).Google Scholar
  9. I. Singer: Abstract Convex Analysis, Wiley, New York (1997).Google Scholar

C. O. Kiselman. “Which Convexity Properties are Preserved under Linear Mappings?.” Journal of Convex Analysis 29 (2022), No. 4, 1023–1035. https://doi.org/10.68381/jca29058