mathematics

James Renegar

James Renegar 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 James Renegar rather than just read about it. In short: James Milton Renegar Jr. (born May 14, 1955) is an American mathematician, specializing in optimization algorithms for linear programming and nonlinear programming.

Key takeaways

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

Reference excerpt

James Milton Renegar Jr. (born May 14, 1955) is an American mathematician, specializing in optimization algorithms for linear programming and nonlinear programming.

Biography In 1983 he received his Ph.D. in mathematics from the University of California, Berkeley. His Ph.D. thesis On the Computational Complexity of Simplicial Algorithms in Approximation Zeros of Complex Polynomials was supervised by Stephen Smale. After postdoc positions, Renegar joined in 1987 the faculty of the School of Operations Research and Information Engineering at Cornell University and is now a full professor there. Renegar is a leading expert on optimization algorithms. In recent years, the focus of his research is devising new algorithms for linear programming. His 2001 monograph A Mathematical View of Interior-point Methods in Convex Optimization is intended to present a general theory of interior-point methods, suitable for a wide audience of graduate students in mathematics and engineering. In 1990 Renegar was an invited speaker at the International Congress of Mathematicians in Kyoto. In 1995 he was a founding member of the nonprofit organization Foundations of Computational Mathematics. He was awarded the 2018 Khachiyan Prize. James M. Renegar Jr. married Catharine M. Barnaby and is the father of two children, Alice and Nicholas James. James M. Renegar Sr. (1928–2005) practiced law in Oklahoma City for many years.

Selected publications

Articles Renegar, James (1987). "On the worst-case arithmetic complexity of approximating zeros of polynomials". Journal of Complexity. 3 (2): 90–113. doi:10.1016/0885-064X(87)90022-7. Renegar, J. (1987). "On the Efficiency of Newton's Method in Approximating All Zeros of a System of Complex Polynomials". Mathematics of Operations Research. 12: 121–148. doi:10.1287/moor.12.1.121. Renegar, James (1988). "A polynomial-time algorithm, based on Newton's method, for linear programming". Mathematical Programming. 40–40 (1–3): 59–93. doi:10.1007/BF01580724. S2CID 206798056. 1988(over 740 citations) Regenar, James (April 1988). "A faster PSPACE algorithm for deciding the existential theory of the reals" (PDF). Technical Report No. 792. School of Operations Research and Industrial Engineering, College of Engineering, Cornell University. Renegar, James (1989). "On the Worst-Case Arithmetic Complexity of Approximating Zeros of Systems of Polynomials". SIAM Journal on Computing. 18 (2): 350–370. doi:10.1137/0218024. hdl:1813/8631. ISSN 0097-5397. Regenar, James (October 1992). "Some perturbation theory for linear programming" (PDF). Technical Report No. 1038. School of Operations Research and Industrial Engineering, College of Engineering, Cornell University. Renegar, James (1992). "On the Computational Complexity of Approximating Solutions for Real Algebraic Formulae". SIAM Journal on Computing. 21 (6): 1008–1025. doi:10.1137/0221060. hdl:1813/8742. Renegar, James (1992). "On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals". Journal of Symbolic Computation. 13 (3): 255–299. doi:10.1016/S0747-7171(10)80003-3. (over 760 citations) Renegar, James (1992). "On the computational complexity and geometry of the first-order theory of the reals. Part II: The general decision problem. Preliminaries for quantifier elimination". Journal of Symbolic Computation. 13 (3): 301–327. doi:10.1016/S0747-7171(10)80004-5. Renegar, James (1992). "On the computational complexity and geometry of the first-order theory of the reals. Part III: Quantifier elimination". Journal of Symbolic Computation. 13 (3): 329–352. doi:10.1016/S0747-7171(10)80005-7. Renegar, James (1994). "Is It Possible to Know a Problem Instance is Ill-Posed?". Journal of Complexity. 10: 1–56. doi:10.1006/jcom.1994.1001. Renegar, James (1995). "Linear programming, complexity theory and elementary functional analysis". Mathematical Programming. 70 (1–3): 279–351. doi:10.1007/BF01585941. hdl:1813/8974. S2CID 16169970. Renegar, James (1996). "Condition Numbers, the Barrier Method, and the Conjugate-Gradient Method". SIAM Journal on Optimization. 6 (4): 879–912. doi:10.1137/S105262349427532X. hdl:1813/8987. Renegar, James (1998). "Recent Progress on the Complexity of the Decision Problem for the Reals". Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation. pp. 220–241. doi:10.1007/978-3-7091-9459-1_11. hdl:1813/8842. ISBN 978-3-211-82794-9. Peña, J.; Renegar, J. (2000). "Computing approximate solutions for convex conic systems of constraints". Mathematical Programming. 87 (3): 351–383. doi:10.1007/s101070050001. S2CID 28849631. Regenar, James (March 2004). "Hyperbolic programs, and their derivative relaxations" (PDF). Technical Report No. 1406. School of Operations Research and Industrial Engineering, College of Engineering, Cornell University. Renegar, James (2016). "Efficient Subgradient Methods for General Convex Optimization". SIAM Journal on Optimization. 26 (4): 2649–2676. arXiv:1605.08712. doi:10.1137/15M1027371. S2CID 13526624. Renegar, James (2019). "Accelerated first-order methods for hyperbolic programming". Mathematical Programming. 173 (1–2): 1–35. arXiv:1512.07569. doi:10.1007/s10107-017-1203-y. S2CID 16427533. Renegar, James; Grimmer, Benjamin (2021). "A Simple Nearly Optimal Restart Scheme for Speeding up First-Order Methods". Foundations of Computational Mathematics. 22: 211–256. arXiv:1803.00151. doi:10.1007/s10208-021-09502-2. S2CID 53356260.

Books "Front Matter". A Mathematical View of Interior-Point Methods in Convex Optimization. Society for Industrial and Applied Mathematics. 2001. pp. i–vii. doi:10.1137/1.9780898718812.fm. ISBN 978-0-89871-502-6.

References

External links Renegar, James (April 30, 2019). "First-Order Methods and Hyperbolic Programming". YouTube. Simons Institute.

Worked examples

Example 1 — a first encounter with James Renegar

Start with the simplest possible case. Write down what James Renegar 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 James Renegar 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 James Renegar 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 James Renegar

In research: James Renegar 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 James Renegar 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: James Renegar is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James Renegar 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 James Renegar in 20 minutes

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Frequently asked questions

What is James Renegar in simple terms?

James Milton Renegar Jr. (born May 14, 1955) is an American mathematician, specializing in optimization algorithms for linear programming and nonlinear programming.

Why does James Renegar 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 James Renegar?

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 James Renegar.