Tseng made many contributions to
mathematical optimization, publishing many articles and helping to develop quality software that has been widely used. He published over 120 papers in optimization and had close collaborations with several colleagues, including
Dimitri Bertsekas and
Zhi-Quan Tom Luo. Tseng's research subjects include: • Efficient algorithms for structured convex programs and network flow problems, •
Complexity analysis of
interior point methods for
linear programming, •
Parallel and
distributed computing, • Error bounds and convergence analysis of iterative algorithms for optimization problems and
variational inequalities, • Interior point methods and semidefinite relaxations for hard quadratic and matrix optimization problems, and • Applications of large scale optimization techniques in
signal processing and
machine learning. In his research, Tseng gave a new proof for the sharpest complexity result for path-following interior-point methods for linear programming. Furthermore, together with Tom Luo, he resolved a long-standing open question on the convergence of
matrix splitting algorithms for linear complementarity problems and affine variational inequalities. Tseng was the first to establish the convergence of the affine scaling algorithm for linear programming in the presence of degeneracy. Tseng has coauthored (with his Ph.D. advisor,
Dimitri Bertsekas) a publicly available network optimization program, called RELAX, which has been widely used in industry and academia for research purposes. This software has been used by statisticians like Paul R. Rosenbaum and
Donald Rubin in their work on
propensity score matching. Tseng's software for matching has similarly been used in
nonparametric statistics to implement
exact tests. Tseng has also developed a program called ERELAXG, for network optimization problems with gains. In 2010 conferences in his honor were held at the University of Washington and at
Fudan University in Shanghai. Tseng's personal web page can be accessed in the exact state it was at the time of his disappearance, and contains many of his writings. ==Travels and disappearance==