Convex set (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Convex set" in English language version.

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Meyer, Robert (1970). "The validity of a family of optimization methods" (PDF). SIAM Journal on Control and Optimization. 8: 41–54. doi:10.1137/0308003. MR 0312915..
Singer, Ivan (1997). Abstract convex analysis. Canadian Mathematical Society series of monographs and advanced texts. New York: John Wiley & Sons, Inc. pp. xxii+491. ISBN 0-471-16015-6. MR 1461544.
For the commutativity of Minkowski addition and convexification, see Theorem 1.1.2 (pages 2–3) in Schneider; this reference discusses much of the literature on the convex hulls of Minkowski sumsets in its "Chapter 3 Minkowski addition" (pages 126–196): Schneider, Rolf (1993). Convex bodies: The Brunn–Minkowski theory. Encyclopedia of mathematics and its applications. Vol. 44. Cambridge: Cambridge University Press. pp. xiv+490. ISBN 0-521-35220-7. MR 1216521.
Zălinescu, C. (2002). Convex analysis in general vector spaces. River Edge, NJ: World Scientific Publishing Co., Inc. p. 7. ISBN 981-238-067-1. MR 1921556.
van De Vel, Marcel L. J. (1993). Theory of convex structures. North-Holland Mathematical Library. Amsterdam: North-Holland Publishing Co. pp. xvi+540. ISBN 0-444-81505-8. MR 1234493.

archive.org

McConnell, Jeffrey J. (2006). Computer Graphics: Theory Into Practice. p. 130. ISBN 0-7637-2250-2..
For the commutativity of Minkowski addition and convexification, see Theorem 1.1.2 (pages 2–3) in Schneider; this reference discusses much of the literature on the convex hulls of Minkowski sumsets in its "Chapter 3 Minkowski addition" (pages 126–196): Schneider, Rolf (1993). Convex bodies: The Brunn–Minkowski theory. Encyclopedia of mathematics and its applications. Vol. 44. Cambridge: Cambridge University Press. pp. xiv+490. ISBN 0-521-35220-7. MR 1216521.
Zălinescu, C. (2002). Convex analysis in general vector spaces. River Edge, NJ: World Scientific Publishing Co., Inc. p. 7. ISBN 981-238-067-1. MR 1921556.

arxiv.org

Brandenberg, René; González Merino, Bernardo (2017). "A complete 3-dimensional Blaschke-Santaló diagram". Mathematical Inequalities & Applications (2): 301–348. arXiv:1404.6808. doi:10.7153/mia-20-22. ISSN 1331-4343.

books.google.com

Morris, Carla C.; Stark, Robert M. (24 August 2015). Finite Mathematics: Models and Applications. John Wiley & Sons. p. 121. ISBN 9781119015383. Retrieved 5 April 2017.
Takayama, Akira (1994). Analytical Methods in Economics. University of Michigan Press. p. 54. ISBN 9780472081356. An often seen confusion is a "concave set". Concave and convex functions designate certain classes of functions, not of sets, whereas a convex set designates a certain class of sets, and not a class of functions. A "concave set" confuses sets with functions.
Corbae, Dean; Stinchcombe, Maxwell B.; Zeman, Juraj (2009). An Introduction to Mathematical Analysis for Economic Theory and Econometrics. Princeton University Press. p. 347. ISBN 9781400833085. There is no such thing as a concave set.

doi.org

Kjeldsen, Tinne Hoff. "History of Convexity and Mathematical Programming" (PDF). Proceedings of the International Congress of Mathematicians (ICM 2010): 3233–3257. doi:10.1142/9789814324359_0187. Archived from the original (PDF) on 2017-08-11. Retrieved 5 April 2017.
Meyer, Robert (1970). "The validity of a family of optimization methods" (PDF). SIAM Journal on Control and Optimization. 8: 41–54. doi:10.1137/0308003. MR 0312915..
Lassak, M. (1993). "Approximation of convex bodies by rectangles". Geometriae Dedicata. 47: 111–117. doi:10.1007/BF01263495. S2CID 119508642.
Brandenberg, René; González Merino, Bernardo (2017). "A complete 3-dimensional Blaschke-Santaló diagram". Mathematical Inequalities & Applications (2): 301–348. arXiv:1404.6808. doi:10.7153/mia-20-22. ISSN 1331-4343.
Theorem 3 (pages 562–563): Krein, M.; Šmulian, V. (1940). "On regularly convex sets in the space conjugate to a Banach space". Annals of Mathematics. Second Series. 41 (3): 556–583. doi:10.2307/1968735. JSTOR 1968735.

ele-math.com

mia.ele-math.com

Brandenberg, René; González Merino, Bernardo (2017). "A complete 3-dimensional Blaschke-Santaló diagram". Mathematical Inequalities & Applications (2): 301–348. arXiv:1404.6808. doi:10.7153/mia-20-22. ISSN 1331-4343.

jstor.org

Theorem 3 (pages 562–563): Krein, M.; Šmulian, V. (1940). "On regularly convex sets in the space conjugate to a Banach space". Annals of Mathematics. Second Series. 41 (3): 556–583. doi:10.2307/1968735. JSTOR 1968735.

mathunion.org

Kjeldsen, Tinne Hoff. "History of Convexity and Mathematical Programming" (PDF). Proceedings of the International Congress of Mathematicians (ICM 2010): 3233–3257. doi:10.1142/9789814324359_0187. Archived from the original (PDF) on 2017-08-11. Retrieved 5 April 2017.

semanticscholar.org

api.semanticscholar.org

Lassak, M. (1993). "Approximation of convex bodies by rectangles". Geometriae Dedicata. 47: 111–117. doi:10.1007/BF01263495. S2CID 119508642.

web.archive.org

Kjeldsen, Tinne Hoff. "History of Convexity and Mathematical Programming" (PDF). Proceedings of the International Congress of Mathematicians (ICM 2010): 3233–3257. doi:10.1142/9789814324359_0187. Archived from the original (PDF) on 2017-08-11. Retrieved 5 April 2017.

wisconsin.edu

minds.wisconsin.edu

Meyer, Robert (1970). "The validity of a family of optimization methods" (PDF). SIAM Journal on Control and Optimization. 8: 41–54. doi:10.1137/0308003. MR 0312915..

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Concave". MathWorld.

worldcat.org

Halmos, Paul R. (8 November 1982). A Hilbert Space Problem Book. Graduate Texts in Mathematics. Vol. 19 (2nd ed.). New York: Springer-Verlag. p. 5. ISBN 978-0-387-90685-0. OCLC 8169781.
Brandenberg, René; González Merino, Bernardo (2017). "A complete 3-dimensional Blaschke-Santaló diagram". Mathematical Inequalities & Applications (2): 301–348. arXiv:1404.6808. doi:10.7153/mia-20-22. ISSN 1331-4343.