mathematics

Philip Wolfe (mathematician)

Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician) rather than just read about it. In short: Philip Starr "Phil" Wolfe (August 11, 1927 – December 29, 2016) was an American mathematician and one of the founders of convex optimization theory and mathematical programming. Life Wolfe received his bachelor's degree, masters, and Ph.D. degrees from the University of California, Berkeley.

Key takeaways

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

Reference excerpt

Philip Starr "Phil" Wolfe (August 11, 1927 – December 29, 2016) was an American mathematician and one of the founders of convex optimization theory and mathematical programming.

Life Wolfe received his bachelor's degree, masters, and Ph.D. degrees from the University of California, Berkeley. He and his wife, Hallie, lived in Ossining, New York.

Career In 1954, he was offered an instructorship at Princeton, where he worked on generalizations of linear programming, such as quadratic programming and general non-linear programming, leading to the Frank–Wolfe algorithm in joint work with Marguerite Frank, then a visitor at Princeton. When Maurice Sion was on sabbatical at the Institute for Advanced Study, Sion and Wolfe published in 1957 an example of a zero-sum game without a minimax value. Wolfe joined RAND corporation in 1957, where he worked with George Dantzig, resulting in the now well known Dantzig–Wolfe decomposition method. In 1965, he moved to IBM's Thomas J. Watson Research Center in Yorktown Heights, New York.

Honors and awards He received the John von Neumann Theory Prize in 1992, jointly with Alan Hoffman.

Selected publications Dantzig, George B.; Wolfe, Philip (February 1960). "Decomposition Principle for Linear Programs". Operations Research. 8 (1): 101–111. doi:10.1287/opre.8.1.101. Frank, M.; Wolfe, P. (1956). "An algorithm for quadratic programming". Naval Research Logistics Quarterly. 3 (1–2): 95–110. doi:10.1002/nav.3800030109. Held, M.; Wolfe, P.; Crowder, H. P. (1974). "Validation of subgradient optimization". Mathematical Programming. 6: 62–88. doi:10.1007/BF01580223. S2CID 206797746. Wolfe, P. (1959). "The Simplex Method for Quadratic Programming". Econometrica. 27 (3): 382–398. doi:10.2307/1909468. JSTOR 1909468.

References

External Information INFORMS: Biography of Philip Wolfe from the Institute for Operations Research and the management Sciences

Worked examples

Example 1 — a first encounter with Philip Wolfe (mathematician)

Start with the simplest possible case. Write down what Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician)

In research: Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician) 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: Philip Wolfe (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1927 births, 2016 deaths, 20th-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Philip Wolfe (mathematician) in simple terms?

Philip Starr "Phil" Wolfe (August 11, 1927 – December 29, 2016) was an American mathematician and one of the founders of convex optimization theory and mathematical programming. Life Wolfe received his bachelor's degree, masters, and Ph.D. degrees from the University of California, Berkeley.

Why does Philip Wolfe (mathematician) 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 Philip Wolfe (mathematician)?

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 Philip Wolfe (mathematician).