%0 Journal Article %T An approximate Hahn–Banach theorem for positively homogeneous functions %+ Vietnam National University, Ho Chi Minh City / Đại học Quốc gia TP. Hồ Chí Minh (VNU-HCM) %+ Institut de Mathématiques de Marseille (I2M) %+ Ets J Soufflet %+ EA2151 Laboratoire de Mathématiques d'Avignon (LMA) %A Dinh, N. %A Ernst, E. %A López, M.A. %A Volle, M. %< avec comité de lecture %@ 0233-1934 %J Optimization %I Taylor & Francis %V 64 %N 5 %P 1321-1328 %8 2015-05-15 %D 2015 %R 10.1080/02331934.2013.864290 %K non-convex Hahn–Banach theorem %K approximate Hahn–Banach theorem %K positively homogeneous functions of degree one %K Fenchel–Legendre conjugate %Z Mathematics [math]/Functional Analysis [math.FA] %Z Mathematics [math]/Classical Analysis and ODEs [math.CA]Journal articles %X This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p such a function defined on the real vector space X, and a linear function l defined on a subspace V of X and dominated by p (i.e. l(x)