Cetraro, July 1-7, 2007
Prof. Immanuel M. Bomze, University of Vienna, Austria
The course will concentrate on a particular class of smooth constrained optimization which allows for enough flexibility to illustrate problems and methods of Global Optimization: standard quadratic optimization.
Moreover, the approach chosen enables students to easily establish connections to topics covered by the other lectures of this course as well: contact points with the presentation by V.Demyanov (Non-smooth optimization) can be found in parts 1 and 4 below; with that by R.Fletcher (Sequential Quadratic Programming) in parts 1 and 2; and with that by T.Terlaky (Interior Point Methods) in parts 3 and 4.
1. The simplest global optimization problems: quadratic optimization
1a. Local versus global optimality; complexity issues2. Some basic techniques, illustrated by StQPs
2a. Escape directions3. Reformulation, relaxation, approximation (again of StQPs)
3a. Unconstrained reformulations4. Approaches to copositivity
4a. Role of copositivity in optimality conditions