title:   Lagrange Multipliers and Duality

speaker:  Henry Wolkowicz

abstract:
In optimization problems, Lagrange multipliers can be applied in two ways. 
One can
use the fact that the optimum lies among the stationary points of the
Lagrangian. However, testing all the stationary points is usually an
inefficient task and/or impossible.

Alternatively, one can relax the problem and try and solve the Lagrangian
dual. This often results in duality gaps. Surprisingly, these gaps can often
be closed by adding redundant constraints to the original problem.
We look at instances with quadratic objectives and constraints.
One example of this is the orthogonal relaxation of the
quadratic assignment problem.