Editing Nonlinear programming (section)

==Applicability==

A typical non-[[Convex optimization|convex]] problem is that of optimizing transportation costs by selection from a set of transportation methods, one or more of which exhibit [[Economy of scale|economies of scale]], with various connectivities and capacity constraints. An example would be petroleum product transport given a selection or combination of pipeline, rail tanker, road tanker, river barge, or coastal tankship. Owing to economic batch size the cost functions may have discontinuities in addition to smooth changes.

In experimental science, some simple data analysis (such as fitting a spectrum with a sum of peaks of known location and shape but unknown magnitude) can be done with linear methods, but in general these problems are also nonlinear.  Typically, one has a theoretical model of the system under study with variable parameters in it and a model the experiment or experiments, which may also have unknown parameters.  One tries to find a best fit numerically.  In this case one often wants a measure of the precision of the result, as well as the best fit itself.