Optimization

Convexity: general results, Convex separation theorem, Farkas’ lemma. Convex polyhedrons. Linear and quadratic programming and applications: Theorem of duality in linear programming, the Frank-Wolfe theorem. Optimal conditions for nonlinear programming: Karush-Kuhn-Tucker conditions, restriction qualifications, saddle points, mini-max conditions. Rockafellar’s duality theory in convex programming. Extensions in convexity: quasi-convexity, pseudo-convexity, etc.

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. – Otimização, 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.

* Standard program. The teacher has the autonomy to make any changes.