Prime Optimization

  • Yuly Shipilevsky
Keywords: Complexity, constraints, optimization, primes, target function

Abstract

This is a pioneering work, introducing a novel class of optimization of objective functions over subsets of primeonly integer points. We show a rich variety of Prime Optimization and mixed problems.

References

M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Annals of Mathematics, vol. 160, pp. 781-793, 2004.

S. Bernstein, U. Kahler, I. Sabadini and F. Sommen, ¨ Hypercomplex Analysis: New Perspectives and Applications, Birkhauser, 2014.

I. V. Blagouchine, Three Notes on Ser’s and Hasse’s Representations for the Zeta functions, INTEGERS: The Electronic Journal of Combinatorial Number Theory, vol. 18A, pp. 1-45, 2018.

L. M. B. C. Campos, Complex Analysis with Applications to Flows and Fields, CRC Press, 2011.

T. Cormen, C. Leiserson, R. Rivest and C. Stein, Introduction To Algorithms, The MIT Press, Cambridge, 2009.

A.W. Dudek, On the Riemann hypothesis and the difference between primes, International Journal of Number Theory, vol. 11, no. 3, pp. 771-778, 2014.

C. A. Floudas and P. M. Pardalos, Encyclopedia of Optimization, Springer, New York, 2009.

I. Frenkel and M. Libine, Quaternionic analysis, representation theory and physics, Advances in Mathematics, vol. 218, pp. 1806- 1877, 2008.

B. Green and T. Tao, Linear equations in primes, Annals of Mathematics, vol.171, pp. 1753-1850, 2010.

R. Hemmecke, M. Koppe, J. Lee and R. Weismantel, ¨ Nonlinear Integer Programming, in 50 Years of Integer Programming 1958- 2008: The Early Years and State-of-the-Art Surveys (eds. M. Junger, T. Liebling, D. Naddef, W. Pulleyblank, W. Reinelt, G. Rinaldi and Wolsey), Springer-Verlag, Berlin, pp. 561-618, 2010.

G. James, Modern Engineering Mathematics, Trans-Atlantic Pubns Inc., 2015.

I. Kleiner, From Numbers to Rings: The Early History of Ring Theory, Elem. Math, Birkhauser, Basel, vol. 53, pp. 18-35, 1998.

E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons Inc., 2011.

V. Neale, Closing the Gap: The Quest to Understand Prime Numbers, Oxford University Press, 2017.

V. Scheidemann, Introduction to complex analysis in several variables, Birkhauser, 2005.

W. T. Shaw, Complex Analysis with Mathematica, Cambridge, 2006.

Y. Shipilevsky, Complex and quaternionic optimization, Numerical Algebra, Control and Optimization, vol.10, no. 3, pp. 249-255, 2020.

Published
2021-06-28
How to Cite
Shipilevsky, Y. (2021). Prime Optimization. Statistics, Optimization & Information Computing, 9(2), 453-458. https://doi.org/10.19139/soic-2310-5070-1063
Section
Research Articles