mathematics

Naum Z. Shor

Naum Z. Shor 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 Naum Z. Shor rather than just read about it. In short: Naum Zuselevich Shor (Russian: Наум Зуселевич Шор) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian mathematician specializing in optimization. He made significant contributions to nonlinear and stochastic programming, numerical techniques for non-smooth optimization, discrete optimization problems, matrix optimization, dual quadratic bounds in multi-extremal programming problems.

Key takeaways

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

Reference excerpt

Naum Zuselevich Shor (Russian: Наум Зуселевич Шор) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian mathematician specializing in optimization. He made significant contributions to nonlinear and stochastic programming, numerical techniques for non-smooth optimization, discrete optimization problems, matrix optimization, dual quadratic bounds in multi-extremal programming problems. Shor became a full member of the National Academy of Science of Ukraine in 1998.

Subgradient methods

N. Z. Shor is well known for his method of generalized gradient descent with space dilation in the direction of the difference of two successive subgradients (the so-called r-algorithm), that was created in collaboration with Nikolay G. Zhurbenko. The ellipsoid method was re-invigorated by A.S. Nemirovsky and D.B. Yudin, who developed a careful complexity analysis of its approximation properties for problems of convex minimization with real data. However, it was Leonid Khachiyan who provided the rational-arithmetic complexity analysis, using an ellipsoid algorithm, that established that linear programming problems can be solved in polynomial time. It has long been known that the ellipsoidal methods are special cases of these subgradient-type methods.

R-algorithm Shor's r-algorithm is for unconstrained minimization of (possibly) non-smooth functions, which has been somewhat popular despite an unknown convergence rate. It can be viewed as a quasi-Newton method, although it does not satisfy the secant equation. Although the method involves subgradients, it is distinct from his so-called subgradient method described above.

References

Notes

Bibliography "Congratulations to Naum Shor on his 65th birthday", Journal of Global Optimization, 24 (2): 111–114, 2002, doi:10.1023/A:1020215832722, S2CID 195226482.

External links ORB Newsletter Issue 5 contains an article with a short biography Video on YouTube

Worked examples

Example 1 — a first encounter with Naum Z. Shor

Start with the simplest possible case. Write down what Naum Z. Shor 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 Naum Z. Shor 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 Naum Z. Shor 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 Naum Z. Shor

In research: Naum Z. Shor 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 Naum Z. Shor 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: Naum Z. Shor is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, 2006 deaths, 20th-century Ukrainian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Naum Z. Shor 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 Naum Z. Shor in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Naum Z. Shor 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 Naum Z. Shor out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Naum Z. Shor in simple terms?

Why does Naum Z. Shor 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 Naum Z. Shor?

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 Naum Z. Shor.