How to Transform One Convex Function Continuously into Another

@article{Bauschke2008HowTT,
  title={How to Transform One Convex Function Continuously into Another},
  author={Heinz H. Bauschke and Yves Lucet and Michael Trienis},
  journal={SIAM Review},
  year={2008},
  volume={50},
  pages={115-132}
}
The proximal average operator provides a parametric family of convex functions that continuously transform one convex function into another even when the domains of the two functions do not intersect. We prove that the proximal average operator is a homotopy with respect to the epi-topology, study its properties, and present several explicit formulas for specific classes of functions. The parametric family inherits desirable properties such as differentiability and strict convexity from the… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 11 extracted citations

A Proximal Average for Nonconvex Functions: A Proximal Stability Perspective

SIAM Journal on Optimization • 2009
View 7 Excerpts
Highly Influenced

The NC-proximal average for multiple functions

Optimization Letters • 2014
View 3 Excerpts
Highly Influenced

Convexity of the Proximal Average

J. Optimization Theory and Applications • 2011
View 3 Excerpts

References

Publications referenced by this paper.
Showing 1-10 of 22 references

Variational Analysis

R. Tyrrell Rockafellar, Roger J-B Wets
1970
View 6 Excerpts
Highly Influenced

Image d’une somme d’opérateurs monotones et applications

H. Brézis, A. Haraux
Israel J. Math., 23 • 1976
View 3 Excerpts
Highly Influenced

Isometries for the Legendre-fenchel Transform

ROGER J. B. WETS
2008
View 1 Excerpt

Convexity and Well-posed Problems

R. Lucchetti
CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 22, Springer, New York • 2006
View 1 Excerpt

Trienis, The piecewise linear-quadratic model for computational convex analysis, tech

Y. Lucet, H. H. Bauschke
2006
View 1 Excerpt

Symbolic convex analysis

C. H. Hamilton
Master’s thesis, Simon Fraser University • 2005
View 1 Excerpt

A brief manual to using Lucet’s code, tech. report, University of Guelph

A. J. Jarvis
2004

Convex Optimization

S. Boyd, L. Vandenberghe
Cambridge University Press, Cambridge • 2004

Projection and proximal point methods: Convergence results and counterexamples

H. H. Bauschke, E. Matoušková, S. Reich
Nonlinear Anal., 56 • 2004
View 1 Excerpt

Similar Papers

Loading similar papers…