Convex functions, Separation theorems, Krein-Milman theorem, Reflexivity, Directional derivatives, Sub-gradients, Convex programs, Kuhn-Tucker theory, Lagrange multipliers, Conjugate functions, The Fenchel-duality theorem, Augmented Lagrange multipliers, Ekeland's variational principle, Phelps extremization principle, Clarke Generalized Derivative, Normal Subdifferential, cone, derivative and its application to optimization.

To introduce students about convex analysis and variational analysis its theories.

To introduces its application to different types of real world optimization problems.

To emphasize both finite and infinite dimensional spaces (Banach or Hilbert spaces).

students should learn convex analysis and variational analysis and its theories and applications in both finite and infinite dimensional spaces (Banach or Hilbert spaces).

R. T. Rockafellar and J. B. R. Wets, Variational Analysis, Springer

B. S. Mordukhovich, Variational Analysis and Generalized differentiation I, Springer

F. H. Clarke, Optimization and Non-smooth Analysis, SIAM

R. T. Rockafellar, Convex Analysis, Princeton University Press