One-Dimensional Optimization


Three general classes of nonlinear optimization problems can be identified, as follows:
  1. 1.

    One-dimensional unconstrained problems

  2. 2.

    Multidimensional unconstrained problems

  3. 3.

    Multidimensional constrained problems

Problems of the first class are the easiest to solve whereas those of the third class are the most difficult. In practice, multidimensional constrained problems are usually reduced to multidimensional unconstrained problems which, in turn, are reduced to one-dimensional unconstrained problems. In effect, most of the available nonlinear programming algorithms are based on the minimization of a function of a single variable without constraints. Therefore, efficient one-dimensional optimization algorithms are required, if efficient multidimensional unconstrained and constrained algorithms are to be constructed.


Line Search Interpolation Formula Unimodal Function Fibonacci Sequence Successive Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2007

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