Optimization Toolbox is an optimization software package developed by MathWorks. It is an add-on product to

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...

, and provides a library of solvers that can be used from the MATLAB environment. The toolbox was first released for MATLAB in 1990.

Optimization algorithms

Optimization Toolbox has algorithms for: *

Linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is ...

* Mixed-integer linear programming *

Quadratic programming Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constr ...

Nonlinear programming In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or st ...

Linear least squares Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and ...

Nonlinear least squares Non-linear least squares is the form of least squares analysis used to fit a set of ''m'' observations with a model that is non-linear in ''n'' unknown parameters (''m'' ≥ ''n''). It is used in some forms of nonlinear regression. The ...

* Nonlinear equation solving *

Multi-objective optimization Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with ...

Applications

Engineering Optimization

Optimization Toolbox solvers are used for engineering applications in MATLAB, such as optimal control and optimal mechanical designs.

Parameter Estimation

Optimization can help with fitting a model to data, where the goal is to identify the model parameters that minimize the difference between simulated and experimental data. Common parameter estimation problems that are solved with Optimization Toolbox include estimating material parameters and estimating coefficients of

ordinary differential equations In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contras ...

Computational Finance

Portfolio optimization Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minim ...

, cashflow matching, and other computational finance problems are solved with Optimization Toolbox.

Utilities and Energy

Optimization Toolbox solvers are used for security constrained optimal power flow and power systems analysis.

Optimization algorithms

Applications

Engineering Optimization

Parameter Estimation

Computational Finance

Utilities and Energy

See also

References

Further reading