Prof. V. Jeyakumar
In this seminar I will talk about semi-definite relaxation approaches for examining and solving classes of difficult global polynomial optimization problems. I will also discuss the associated approximation schemes for studying bi-level global polynomial optimization problems. In addition to the usual tools of nonlinear optimization, such as convex analysis and linear algebra, powerful techniques of real algebraic geometry allow us to examine and solve hard global optimization problems involving polynomials. What has real algebraic geometry to do with optimization? The answer is: quite a lot. And all this is due to innovative ideas and links discovered in the last two decades between pure and applied mathematics. A good understanding of convexity in real algebraic geometry will lead to insights into solving hard global optimization problems.