Constructive convex programming

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandBeitrag in Buch/SammelwerkForschungPeer-Review

Autoren

  • Josef Berger
  • G. Svindland

Externe Organisationen

  • Ludwig-Maximilians-Universität München (LMU)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Titel des SammelwerksProof and Computation
UntertitelDigitization in Mathematics, Computer Science and Philosophy
Seiten53-82
Seitenumfang30
ISBN (elektronisch)9789813270947
PublikationsstatusVeröffentlicht - 2018
Extern publiziertJa

Abstract

Working within Bishop-style constructive mathematics, we show that positive-valued, uniformly continuous, convex functions defined on convex and compact subsets of Rn have positive infimum. This gives rise to a separation theorem for convex sets. Based on these results, we show that the fundamental theorem of asset pricing is constructively equivalent to Markov’s principle. The philosophical background behind all this is a constructively valid convex version of Brouwer’s fan theorem. The emerging comprehensive yet concise overall picture of assets, infima of functions, separation of convex sets, and the fan theorem indicates that mathematics in convex environments has some innate constructive nature.

ASJC Scopus Sachgebiete

Zitieren

Constructive convex programming. / Berger, Josef; Svindland, G.
Proof and Computation: Digitization in Mathematics, Computer Science and Philosophy. 2018. S. 53-82.

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandBeitrag in Buch/SammelwerkForschungPeer-Review

Berger, J & Svindland, G 2018, Constructive convex programming. in Proof and Computation: Digitization in Mathematics, Computer Science and Philosophy. S. 53-82. https://doi.org/10.1142/9789813270947_0002
Berger, J., & Svindland, G. (2018). Constructive convex programming. In Proof and Computation: Digitization in Mathematics, Computer Science and Philosophy (S. 53-82) https://doi.org/10.1142/9789813270947_0002
Berger J, Svindland G. Constructive convex programming. in Proof and Computation: Digitization in Mathematics, Computer Science and Philosophy. 2018. S. 53-82 doi: 10.1142/9789813270947_0002
Berger, Josef ; Svindland, G. / Constructive convex programming. Proof and Computation: Digitization in Mathematics, Computer Science and Philosophy. 2018. S. 53-82
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