Optimization Toolbox 

Optimization Toolbox can solve largescale linear and quadratic programming problems.
Linear programming problems involve minimizing or maximizing a linear objective function subject to bounds, linear equality, and inequality constraints. Linear programming is used in finance, energy, operations research, and other applications where relationships between variables can be expressed linearly.
Optimization Toolbox includes three algorithms used to solve linear programming problems:
Quadratic programming problems involve minimizing a multivariate quadratic function subject to bounds, linear equality, and inequality constraints. Quadratic programming is used for portfolio optimization in finance, power generation optimization for electrical utilities, design optimization in engineering, and other applications.
Optimization Toolbox includes three algorithms for solving quadratic programs:
Optimization in MATLAB: An Introduction to Quadratic Programming
36:35
In this webinar, you will learn how MATLAB can be used to solve optimization problems using an example quadratic optimization problem and the symbolic math tools in MATLAB.
Both the interiorpointconvex and trustregionreflective algorithms are large scale, meaning they can handle large, sparse problems. Furthermore, the interiorpointconvex algorithm has optimized internal linear algebra routines and a new presolve module that can improve speed, numerical stability, and the detection of infeasibility.