Geodesic
Continuous Convex $\mathrm{MS}$-Differentiable Function Need not Be $\mathrm{HL}$-Differentiable
Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 163-171

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We construct here an example of a continuous convex function on a locally convex space, which is $\mathrm{MS}$-differentiable at a point, but is not $\mathrm{HL}$-differentiable at this point.
Keywords: topological vector space, convex function, $\mathrm{MS}$-differentiability, $\mathrm{HL}$-differentiability, Fréchet differentiability, balanced absorbing subset, Minkowski function. 
@article{MZM_2012_91_2_a0,
     author = {V. I. Averbukh and T. Konderla},
     title = {Continuous {Convex} $\mathrm{MS}${-Differentiable} {Function} {Need} not {Be} $\mathrm{HL}${-Differentiable}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--171},
     publisher = {mathdoc},
     volume = {91},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a0/}
}
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V. I. Averbukh; T. Konderla. Continuous Convex $\mathrm{MS}$-Differentiable Function Need not Be $\mathrm{HL}$-Differentiable. Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 163-171. http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a0/