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Approximation and Complexity

In: Non-Convex Multi-Objective Optimization

Author

Listed:
  • Panos M. Pardalos

    (University of Florida
    Research University Higher School of Economics)

  • Antanas Žilinskas

    (Vilnius University)

  • Julius Žilinskas

    (Vilnius University)

Abstract

In computer science, the theory of computational complexity was developed to evaluate the hardness of problems, regarding the number of steps to obtain a solution; for the basic results of that theory we refer to [147]. The model of computations, used in that theory, is either the Turing machine or any other equivalent model. The input and output of the Turing machine should be encoded as finite strings of bits. Such an encoding can be used to represent the objects of discrete nature, and the theory of computational complexity is favorable, e.g., to the investigation of problems of single-objective combinatorial optimization [150, 151]. However, the Turing machine model is not suitable for the algorithms using real numbers. Therefore alternative complexity theories have been developed for the investigation of problems of continuous nature. For the fundamentals of the complexity of real number algorithms we refer to [19, 218], and for the complexity of problems of mathematical programming to [143, 150, 151].

Suggested Citation

  • Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Approximation and Complexity," Springer Optimization and Its Applications, in: Non-Convex Multi-Objective Optimization, chapter 0, pages 19-31, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-61007-8_3
    DOI: 10.1007/978-3-319-61007-8_3
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