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Solve linear programming problems

Linear programming solver

Finds the minimum of a problem specified by

$$\underset{x}{\mathrm{min}}{f}^{T}x\text{suchthat}\{\begin{array}{c}A\cdot x\le b,\\ Aeq\cdot x=beq,\\ lb\le x\le ub.\end{array}$$

*f*, *x*, *b*, *beq*, *lb*,
and *ub* are vectors, and *A* and *Aeq* are
matrices.

**Note**

`linprog`

applies only to the solver-based approach. For a discussion
of the two optimization approaches, see First Choose Problem-Based or Solver-Based Approach.

finds the minimum for `x`

= linprog(`problem`

)`problem`

, a structure
described in `problem`

.

You can import a `problem`

structure from an MPS file
using `mpsread`

. You can
also create a `problem`

structure from an
`OptimizationProblem`

object by using
`prob2struct`

.

The **Optimize** Live Editor task provides a visual interface for `linprog`

.

[1] Dantzig, G.B., A. Orden, and P. Wolfe.
“Generalized Simplex Method for Minimizing a Linear Form Under
Linear Inequality Restraints.” *Pacific Journal Math.,* Vol.
5, 1955, pp. 183–195.

[2] Mehrotra, S. “On the Implementation
of a Primal-Dual Interior Point Method.” *SIAM Journal
on Optimization*, Vol. 2, 1992, pp. 575–601.

[3] Zhang, Y., “Solving Large-Scale
Linear Programs by Interior-Point Methods Under the MATLAB Environment.” *Technical
Report TR96-01*, Department of Mathematics and Statistics,
University of Maryland, Baltimore County, Baltimore, MD, July 1995.

`intlinprog`

| `mpsread`

| Optimize | `optimoptions`

| `prob2struct`

| `quadprog`