Abstract
Three general classes of nonlinear optimization problems can be identified, as follows:
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1.
One-dimensional unconstrained problems
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2.
Multidimensional unconstrained problems
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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.
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(2007). One-Dimensional Optimization. In: Practical Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71107-2_4
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DOI: https://doi.org/10.1007/978-0-387-71107-2_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-71106-5
Online ISBN: 978-0-387-71107-2
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