Engineers and scientists use mathematical modeling to describe the behavior of systems under study. System requirements, when defined mathematically as constraints on the decision variables input into the mathematical system model, form a mathematical program. This mathematical program, or optimization problem description, can then be solved using optimization techniques. Linear programming is one class of mathematical programs where the objective and constraints consist of linear relationships.
Mathematical Modeling with Optimization, Part 1
Transform a problem description into a mathematical program that can be solved using optimization, using a steam and electric power plant example.
Mathematical Modeling with Optimization, Part 2
Solve a linear program using Optimization Toolbox™ solvers, using a steam and electric power plant example.
Linear programming problems consist of a linear expression for the objective function and linear equality and inequality constraints. Optimization Toolbox includes three algorithms used to solve this type of problem:
Binary integer programming problems involve minimizing a linear objective function subject to linear equality and inequality constraints. Each variable in the optimal solution must be either a 0 or a 1.
Optimization Toolbox solves these problems using a branch-and-bound algorithm that: