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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 path-following 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 worst-case complexity than known before. The unified analysis preserves the complexity of small-update IPMs while the complexity of large-update 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)


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