Existence of solutions. Optimality conditions for unconstrained problems. Optimality conditions in primal form for problems with constraints. The tangent cone. Optimality conditions for equality constraints (Lagrange conditions, second order conditions). Convex sets. Separation theorems. Alternative theorems. Convex functions. Optimality conditions for equality and inequality constraints (Karush-Kuhn-Tucker conditions, second order conditions). Elements of Duality Theory.

References:
BAZARAA, M. S., SHERALI, H. D., SHETTY, C. M. – Nonlinear programming: Theory and algorithms. 3nd ed. Wiley-Interscience, John Wiley & Sons, Hoboken, NJ, 2006.
BERTSEKAS, D. P. – Nonlinear programming, Belmont, Mass.: Athena Scientific, 1995.
IZMAILOV, A., SOLODOV, M. – Optimization, volume 1: Rio de Janeiro, IMPA, 2005.
LUENBERGER, D. G. – Linear and nonlinear programming. 2nd ed. Kluwer Academic Publishers, Boston, MA, 2003.
PERESSINI, A. L.; SULLIVAN, F. E., UHL, J. J., JR- The mathematics of nonlinear programming. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1988.
ROCKAFELLAR, R. T. – Convex Analysis. Princeton Univ. Press, 1970.

* Basic syllabus. The teacher has the autonomy to make any changes.