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Balanced Integer Solutions of Linear Equations

In: Applications of Mathematics and Informatics in Science and Engineering

Author

Listed:
  • Konstantinos A. Draziotis

    (Aristotle University of Thessaloniki)

Abstract

We use lattice-based methods in order to get an integer solution of the linear equation a 1 x 1 + ⋯ + a n x n = a 0 , $$a_{1}x_{1} + \cdots + a_{n}x_{n} = a_{0},$$ which satisfies the bound constraints | x j | ≤ X j . Further we study the corresponding homogeneous linear equation under constraints and finally we apply our method to Knapsack problem.

Suggested Citation

  • Konstantinos A. Draziotis, 2014. "Balanced Integer Solutions of Linear Equations," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Science and Engineering, edition 127, pages 173-188, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-04720-1_11
    DOI: 10.1007/978-3-319-04720-1_11
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