DIMACS Workshop on Diagonal Matrix Scaling and its Generalizations and Their Applications in Convex Programming Over Cones

August 25 - 26, 1999
DIMACS Center, Rutgers University, Piscataway, NJ

Bahman Kalantari, Rutgers University, kalantari@cs.rutgers.edu
Uriel Rothblum, Technion-Israel Institute of Technology, rothblum@ie.technion.ac.il
Alex Samorodnitsky, DIMACS, Rutgers University, salex@av.rutgers.edu
Presented under the auspices of the DIMACS Special Year on Large Scale Discrete Optimization.

The diagonal matrix scaling problem and its generalizations form a fundamental set of problems in mathematical programming and computer science. On the one hand for nonnegative matrices the doubly stochastic scaling is a fundamental problem in itself with diverse applications, e.g., in estimation of transition probability in Markov chains, network optimization, planning of traffic and transportation, matrix preconditioning, image reconstruction. On the other hand, the doubly quasi-stochastic scaling of positive semidefinite matrices and its generalizations has tremendous theoretical and algorithmic applications in linear programming, semidefinite programming, and more generally self-concordant conic convex programming. Indeed diagonal matrix scaling has played a key role in Karmarkar's famous LP algorithm. The matrix scaling problem also finds application in combinatorial problems as well as in the approximation of NP-complete problems.

The aim of this workshop is to bring together researchers working on theoretical and practical aspects of matrix scaling problems (including matrix balancing), and their generalizations. Hopefully, the workshop will give a more convincing evidence on the broad significance of the matrix scaling problems to researchers within this area, as well as those interested in convex programming, self-concordance theory, duality theory, complexity of algorithms, combinatorial optimization, homogeneous inequalities, numerical analysis, etc. Moreover, the workshop should result in the definition of new research topics and description of open problems.
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Document last modified on August 10, 1999.