YuYing Li

Computational algorithms for optimization problems

Scientific computing involves the design and implementation of numerical methods to solve industrial-sized, continuous problems in finance, health, and engineering. In order to get the best possible outcome, given the variables of a specific situation, optimization theory and techniques are often used. The design and analysis of computational algorithms, specifically for optimization problems, is part of Yuying Li’s work.

Yuying has recently been involved in financial applications, helping companies to evaluate portfolios and design dynamic trading strategies that manage risk in an optimal fashion. These situations require complex algorithms and computational power. Yuying explains: “In finance everything is uncertain and companies, particularly in the insurance industry, are faced with the huge task of evaluating liabilities under stochastic scenarios. These problems are computationally and mathematically challenging.”

The financial industry is interesting to researchers like Yuying because of the number of complex problems that arise within that field — risk model estimation, option price calibration or general portfolio decisions. Similar techniques, however, can be applied to other areas of study. Yuying has designed algorithms that analyze  Computerized Tomography (CT) scans for cancer detection. “It’s still an optimization problem,” she explains. “We’re trying to minimize total variation to best segment cancerous nodules.”

The appeal of scientific computing for Yuying is straightforward. “I enjoy the problem solving aspect; sorting things out, finding the appropriate approach,” she says. “It’s a very satisfying process intellectually. But I’ve always liked looking at the application side, because it’s gratifying when my work has consequence in real life situations.” Yuying is a member of University of Waterloo’s Centre for Computational Mathematics.

University of Waterloo Mathematics, Annual Report 2005