Three general classes of nonlinear optimization problems can be identified, as follows:
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.
One-dimensional unconstrained problems
Multidimensional unconstrained problems
Multidimensional constrained problems
KeywordsLine Search Interpolation Formula Unimodal Function Fibonacci Sequence Successive Interval
Unable to display preview. Download preview PDF.
- 2.B. S. Gottfried and J. Weisman, Introduction to Optimization Theory, Prentice-Hall, Englewood Cliffs, N.J., 1973.Google Scholar
- 4.C. S. Beightler, D. T. Phillips, and D. J. Wilde, Foundations of Optimization, Prentice-Hall, Englewood Cliffs, N.J., 1979.Google Scholar
- 8.M. J. Box, D. Davies, and W. H. Swann, Nonlinear Optimization Techniques, Oliver and Boyd, London, 1969.Google Scholar
© Springer Science+Business Media, LLC 2007