*Wissenschaftliches Programm* *Liste der Vortragenden*
9.00 Uhr, Großer Mathematik-Hörsaal, Trefftz-Bau
Aharon Ben-Tal, MINERVA Optimization Center Technion – Israel Institute of Technology
We briefly describe the evolution of theoretical and computational ideas underlying the progress
in optimization. We then concentrate on three main topics which are at the core of modern
K is one of the three convex cones
(a) Efficiency estimates of algorithms, i.e., bounds on the error induced by an iterative
algorithm at each iteration — in contrast to asymptotic convergence.
(b) Complexity of algorithms, i.e., the number of arithmetic operations needed to solve a
problem within a prescribed error bound — in contrast to asymptotic speed of convergence.
(c) Tractable optimization problems, i.e., problems with specific structure, yet rich in
modeling possibilities, for which efficient polynomial-time algorithms are available.
The central model for tractable problems is the conic convex program
|K = ||n (for which problem (P) is a linear program)
|K = ||the second order (Lorentz) cone|
| ||(for which problem (P) is a conic quadratic program)|
|K = ||the cone of symmetric positive-semi-definite matrices|
We summarize the state-of-the-art complexity theory for problem (P). Finally, we demonstrate the new
possibilities offered by modern optimization methods in other disciplines:
| ||(for which problem (P) is a semi-definite program).|
Combinatorial Optimization (example: the MAXCUT problem);
Dynamic Systems and Control (example: Lyapunov stability of uncertain dynamic systems);
Uncertain Engineering Design (examples: Synthesis array of antennae, truss topology design).