Linear programming (LP),involves minimizing or maximizing a linear objective function subject to bounds, linear equality, and inequality constraints. Example problems include design optimization in engineering, profit maximization in manufacturing, portfolio optimization in finance, and scheduling in energy and transportation.
Linear programming is the mathematical problem of finding a vector \(x\) that minimizes the function:
\[\min_{x} \left\{f^{\mathsf{T}}x\right\}\]
Subject to the contraints:
\[\begin{eqnarray}Ax \leq b & \quad & \text{(inequality constraint)} \\A_{eq}x = b_{eq} & \quad & \text{(equality constraint)} \\lb \leq x \leq ub & \quad & \text{(bound constraint)}\end{eqnarray}\]
The following algorithms are commonly used to solve linear optimization problems:
For more information on algorithms and linear programming, see Optimization Toolbox™.
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See also: Optimization Toolbox, Global Optimization Toolbox, integer programming, quadratic programming, nonlinear programming, multiobjective optimization, genetic algorithm, simulated annealing, prescriptive analytics
In this course you’ll learn applied optimization techniques in the MATLAB^{®} environment, focusing on using Optimization Toolbox™ and Global Optimization Toolbox.