Approximation Optimization Task

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An Approximation Optimization Task is an optimization task where the Optimality requirements are loosened.



  • (Wikipedia, 2009) ⇒
    • An approximation (usually represented by the symbol ≈) is an inexact representation of something that is still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.
    • Approximations may be used because incomplete information prevents use of exact representations. Many problems in physics are either too complex to solve analytically, or impossible to solve using the available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.
    • For instance, physicists often approximate the shape of the Earth as a sphere even though more accurate representations are possible, because many physical behaviours — e.g. gravity — are much easier to calculate for a sphere than for other shapes.

  • (Wikipedia, 2009) ⇒
    • The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because
      • 1. the measurement of the data is not precise (due to the instruments), or
      • 2. approximations are used instead of the real data (e.g., 3.14 instead of π).
    • In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.