Optimization 2010/11

Optimization

Academic Year 2010/11
Spring Semester, PhD Program in Mathematics

News

Instructor

Luís Nunes Vicente
Office 5.12, Departamento de Matemática da FCTUC
Office Hours: Tuesdays and Thursdays (11:30am-1pm)

Schedule

Classes: Fridays (9am-1pm) in Room 2.5-DM

Outline

Basic notions of convex sets and functions. Tangent cone and cone of linearized feasible directions. Constraint qualifications. First-order necessary and sufficient conditions for optimality. Second-order necessary and sufficient conditions for optimality. Basic notions of duality theory. The cases of linear and quadratic programming. Basic notions of multicriteria optimization. Tools and concepts for numerical optimization.

References

Book Followed

J. Nocedal and S. J. Wright, Numerical Optimization, second edition, Springer, Berlin, 2006

Other Books

A. R. Conn, K. Scheinberg, and L. N. Vicente, Introduction to Derivative-Free Optimization, MPS-SIAM Book Series on Optimization, SIAM, Philadelphia, 2009
J. E. Dennis and R. B. Schnabel, Numerical methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, 1996
I. Griva, S. G. Nash, and A. Sofer, Linear and Nonlinear Optimization, second edition, SIAM, Philadelphia, 2009

Grading

The final grade is the average of the grades of the two mid-term exams (March 18 and May 27, both at 10am in Room 2.5-DM) and of the four homework assignments, or the grade of the final exam.