mathematics

Paul Tseng

Paul Tseng is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Paul Tseng rather than just read about it. In short: Paul Tseng (Chinese: 曾匀) was a Taiwanese-born American-Canadian applied mathematician and a professor at the Department of Mathematics at the University of Washington, in Seattle, Washington. Tseng was recognized by his peers to be one of the leading optimization researchers of his generation.

Key takeaways

Paul Tseng belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Paul Tseng to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Paul Tseng from memory before moving on to harder problems.

Reference excerpt

Paul Tseng (Chinese: 曾匀) was a Taiwanese-born American-Canadian applied mathematician and a professor at the Department of Mathematics at the University of Washington, in Seattle, Washington. Tseng was recognized by his peers to be one of the leading optimization researchers of his generation. On August 13, 2009, Paul Tseng went missing while kayaking in the Jinsha River in the Yunnan province of China and is presumed dead.

Biography Tseng was born September 21, 1959, in Hsinchu, Taiwan. In December 1970, Tseng's family moved to Vancouver, British Columbia. Tseng received his B.Sc. from Queen's University in 1981 and his Ph.D. from Massachusetts Institute of Technology in 1986. In 1990 Tseng moved to the University of Washington's Department of Mathematics. Tseng has conducted research primarily in continuous optimization and secondarily in discrete optimization and distributed computation.

Research 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 Paul Tseng was an ardent bicyclist, kayaker and backpacker. He took many adventurous trips, including kayak tours along the Mekong, the Danube, the Nile and the Amazon. On August 13, 2009, Paul Tseng went missing while kayaking in the Yantze river near Lijiang, in Yunnan province of China and is now presumed dead.

Illustrations

Worked examples

Example 1 — a first encounter with Paul Tseng

Start with the simplest possible case. Write down what Paul Tseng claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Paul Tseng before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Paul Tseng ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Paul Tseng

In research: Paul Tseng appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Paul Tseng in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Paul Tseng is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 2000s missing person cases, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Tseng outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Paul Tseng in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Paul Tseng means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Paul Tseng out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Paul Tseng in simple terms?

Why does Paul Tseng matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Paul Tseng?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Paul Tseng.