Abstract
In general, constrained optimization problems can be written as
where x ∈ R n, f : R n → R 1, h : R n → R m and g : R n → R q. The simplest form of this problem is realized when the functions f(x), h(x) and g(x) are all linear in x. The resulting model is known as a linear program (LP) and plays a central role in virtually every branch of optimization. Many real situations can be formulated or approximated as LPs, optimal solutions are relatively easy to calculate, and computer codes for solving very large instances consisting of millions of variables and tens of thousands of constraints are commercially available. Another attractive feature of linear programs is that various subsidiary questions related, for example, to the sensitivity of the optimal solution to changes in the data and the inclusion of additional variables and constraints can be analyzed with little effort.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bard, J.F. (1998). Linear Programming. In: Practical Bilevel Optimization. Nonconvex Optimization and Its Applications, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2836-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2836-1_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4807-6
Online ISBN: 978-1-4757-2836-1
eBook Packages: Springer Book Archive