CETVRTAK, 01. oktobar 2009. u 14 sati: (ZAJEDNICKI SASTANAK OBA ODELJENJA)


Andreas Griewank, Humboltd University Berlin
DERIVATIVE-BASED OPTIMIZATION

Abstract: Since Cauchy's time standard optimization methods require the evaluation of first derivatives for objective and constraint functions. At least the existence of these gradients and Jacobians is typically needed to ensure convergence for any optimization method that does not simply cover the feasible domain with sample points. The latter shot-gun approach is clearly unsuitable for high-dimensional problems of current interest. To beat the 'curse of dimensionality' in nonlinear optimization one can exploit the fact that continuous and discrete adjoints alike yield first and second derivative vectors at costs proportional to the underlying function and constraint evaluations. We discuss the resulting 'selective derivative methods' in comparison to derivative-free-methods in terms of numerical efficiency, applicability, and user convenience. Finally we report numerical experiences from aerodynamics and oceanography as depicted on the graph.

Petak, 23. 10. 2009. u 14h sala 301f MI SANU

Vladimir Bozovic, Univerzitet u Podgorici
FAKTORIZACIJA KONACNIH GRUPA

Apstrakt: Pod faktorizacijom konacne grupe $G$ podrazumijevamo kolekciju njenih podskupova $[B_1, B_2, ..., B_k]$ tako da se svaki element $g \in G$ moze predstaviti na jedinistven nacin $g = s_1s_2 \cdot\cdot\cdot s_k$, $s_i \in Bi$, $1 \leq i \leq k$. Grupovne faktorizacije, kao veoma privlacna tema na teorijskom nivou, se pojavljuje u aplikacijama, i to u kriptografji, teoriji grafova i kodiranja. Konstrukcija i opis faktorizacija za datu grupu su u principu teski problemi, koji su samo u specijalnim slucajevima potpuno rijeseni. To se posebno odnosi na neke komutativne grupe. Predstavicemo elemente teorije grupovnih faktorizacija i dati pregled osnovnih rezultata. Posebno, neki novi rezultati u faktorizaciji nekomutativnih grupa ce biti prezentovani.