Murray Marshall
University of Saskatchewan, Saskatoon
Part 1: Polynomial optimization via semidefinite programming
1. General representation theorem for partially ordered commutative
rings.
2. The locally convex topology on $R[X]/I$. Duality theorem for convex
cones.
3. Multi-dimensional moment problem. Moment sequences.
4. Optimization via semidefinite programming (global, on an algebraic
set, on a basic closed semialgebraic set).
5. Stability questions.
Part 2: Optimization of a quadratic polynomial on the discrete hypercube
1. Goemans-Williamson error estimate.
2. Nesterov's error estimates.
3. Other error estimates.
4. Open problem.