The Proximal Average: Basic Theory

@article{Bauschke:2008, abstract = {The recently introduced proximal average of two convex functions is a convex function with many useful properties. In this paper, we introduce and systematically study the proximal average for finitely many convex functions. The basic properties of the proximal average with respect to the standard convex-analytical notions (domain, Fenchel conjugate, subdifferential, proximal mapping, epi-continuity, and others) are provided and illustrated by several examples.}, author = {Bauschke, Heinz H. and Goebel, Rafal and Lucet, Yves and Wang, Xianfu}, citeulike-article-id = {3319735}, comment = {Includes a nice summary of epi-addition and multiplication and their properties as well as their relationships with the Fenchel dual.}, journal = {SIAM Journal on Optimization}, keywords = {average, convexity, fenchel\_duality, theory}, number = {2}, pages = {766--785}, posted-at = {2008-09-23 04:37:54}, priority = {4}, publisher = {SIAM}, title = {The Proximal Average: Basic Theory}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOPE8000019000002000766000001&idtype=cvips&gifs=yes}, volume = {19}, year = {2008} }

TY - JOUR ID - Bauschke:2008 L3 - citeulike-article-id:3319735 N2 - The recently introduced proximal average of two convex functions is a convex function with many useful properties. In this paper, we introduce and systematically study the proximal average for finitely many convex functions. The basic properties of the proximal average with respect to the standard convex-analytical notions (domain, Fenchel conjugate, subdifferential, proximal mapping, epi-continuity, and others) are provided and illustrated by several examples. IS - 2 JF - SIAM Journal on Optimization EP - 785 TI - The Proximal Average: Basic Theory PB - SIAM VL - 19 SP - 766 KW - average KW - convexity KW - fenchel_duality KW - theory N1 - Includes a nice summary of epi-addition and multiplication and their properties as well as their relationships with the Fenchel dual. AU - Bauschke, Heinz AU - Goebel, Rafal AU - Lucet, Yves AU - Wang, Xianfu PY - 2008/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOPE8000019000002000766000001&idtype=cvips&gifs=yes ER -