Linear Programming

  • Jonathan F. Bard
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 30)


In general, constrained optimization problems can be written as
$$\min \left\{ {f\left( x \right):h\left( x \right) = 0,g\left( x \right)0} \right\}$$
where xR 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.


Feasible Solution Extreme Point Simplex Method Slack Variable Simplex Algorithm 
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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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Jonathan F. Bard
    • 1
  1. 1.Graduate Program in Operations Research, Department of Mechanical EngineeringThe University of TexasAustinUSA

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