MATH-731: Convex Analysis

Convex functions on the real line, Continuity and differentiability of convex functions, Characterizations, Differences of convex functions, Conjugate convex functions, Convex sets and affine sets, Convex functions on a normed linear space, Continuity of convex functions on normed linear space, Differentiable convex function on normed linear space, The support of convex functions, Differentiability of convex function on normed linear space.

1. Jonathan M. Borwein and Adrian S. Lewis, Convex Analysis and Nonlinear Optimization: Theory and Examples (CMS Books in Mathematics), 2nd Edition, Springer, 2010.
2. A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973.
3. C. P. Niculescu, L-E. Persson, Convex Functions and Their Applications, Springer verlag New York, 2006.
4. R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, N.J., 1970.
5. Related research papers