




Operations Research 2) Mathematical Programming / Programmation
mathématique
 ALLEN HOLDER, Trinity University
Radiotherapy planning via linear optimization

Radiotherapy is the treatment of tumors by external beams of electrons
or photons. A treatment plan consists of a collection of beam angles,
intensities along these angles, and shielding information. Because
modern treatment facilities are capable of implementing complicated
treatment plans, modeling software is needed to obtain desirable
plans. A new linear optimization model is developed that produces
treatment plans that guarantee a uniform dose over the tumor and that
critical structures are damaged as little as possible. Moreover, we
show that the analytic center solution produced from a pathfollowing
interior point algorithm has favorable characteristics.
 TAMÁS TERKALY, Department of Computing and Software, McMaster University
New proximities and search directions for linear and semidefinite
optimization

Various potential functions have been used in the design and analysis
of interior point methods (IPMs). Usually, these functions are driven
from a barrier function of one variable with some desirable
properties. Most barrier functions in the IPM literature are related
to the logarithmic barrier function. Here, a new class of barrier
functions is introduced. Their growth behavior and barrier property
will be discussed. Interior point methods based on the new barrier
functions enjoy better worstcase complexity than known before. The
unified analysis preserves the complexity of smallupdate IPMs while
the complexity of largeupdate IPMs gets 0(n^{[(q+1)/(2q)]} where
q is nonnegative. (Joint work with J. Peng (Y. U. Delft and
McMaster) and C. Roos (TU Delft)

