70 OP11 Abstracts IP1 general. Moreover, box constraints on the state function Sparse Optimization are also admitted. Later, the model is improved by in- cluding Maxwell equations for induction heating and state Many computational problems of recent interest can be constraints on the generated temperature. Also the com- formulated as optimization problems that contain an un- pletion of the model by Navier-Stokes equations in a melt is derlying objective together with regularization terms that briefly mentioned. For these problems, the well-posedness promote a particular type of structure in the solution. of the underlying systems of PDEs and the principal form Since a commonly desired property is that the vector of of optimality conditions are sketched. Numerical examples unknowns should have relatively few nonzeros (a “sparse illustrate the theory, justify certain simplifications and and vector’), the term “sparse optimization’ is used as a broad motivate the necessity of more complex models. Finally, label for the area. These problems have arisen in machine ongoing research on applications to industrial processes of learning, image processing, compressed sensing, and sev- crystal growth is briefly addressed. eral other fields. This talk surveys several applications that can be formulated and solved as sparse optimization Fredi Tr¨oltzsch problems, highlighting the novel ways in which algorithms Technische Universit¨at, Berlin have been assembled from a wide variety of optimization
[email protected] techniques, old and new. Stephen Wright IP4 University of Wisconsin Matrix Optimization: Searching Between the First Dept. of Computer Sciences andSecondOrderMethods
[email protected] During the last two decades, matrix optimization prob- lems (MOPs) have undergone rapid developments due to IP2 their wide applications as well as their mathematical ele- Optimizing Radiation Therapy - Past Accomplish- gance.