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Optimization Decision Table

The following table is designed to help you choose a solver. It does not address multiobjective optimization or equation solving. There are more details on all the solvers in Problems Handled by Optimization Toolbox Functions.

In this table:

* means relevant solvers are found in Global Optimization Toolbox (Global Optimization Toolbox) functions (licensed separately from Optimization Toolbox™ solvers).
fmincon applies to most smooth objective functions with smooth constraints. It is not listed as a preferred solver for least squares or linear or quadratic programming because the listed solvers are usually more efficient.
The table has suggested functions, but it is not meant to unduly restrict your choices. For example, fmincon can be effective on some nonsmooth problems.
The Global Optimization Toolbox ga (Global Optimization Toolbox) and surrogateopt (Global Optimization Toolbox) functions can address mixed-integer nonlinear programming problems.
The Statistics and Machine Learning Toolbox™ bayesopt (Statistics and Machine Learning Toolbox) function can address low-dimensional deterministic or stochastic optimization problems with combinations of continuous, integer, or categorical variables.

Solvers by Objective and Constraint

Constraint Type	Objective Type
Constraint Type	Linear	Quadratic	Least Squares	Smooth Nonlinear	Nonsmooth
None	n/a (f = const, or min = $- \infty$ )	`quadprog`, Information	`mldivide`, `lsqcurvefit`, `lsqnonlin`, Information	`fminsearch`, `fminunc`, Information	`fminsearch`, *
Bound	`linprog`, Information	`quadprog`, Information	`lsqcurvefit`, `lsqlin`, `lsqnonlin`, `lsqnonneg`, Information	`fminbnd`, `fmincon`, `fseminf`, Information	`fminbnd`, *
Linear	`linprog`, Information	`quadprog`, Information	`lsqcurvefit`, `lsqlin`, `lsqnonlin`, Information	`fmincon`, `fseminf`, Information	*
Cone	`coneprog`, Information	`fmincon`, Information	`lsqcurvefit`, `fmincon`, `lsqnonlin`, Information	`fmincon`, Information	*
General Smooth	`fmincon`, Information	`fmincon`, Information	`lsqcurvefit`, `fmincon`, `lsqnonlin`, Information	`fmincon`, `fseminf`, Information	*
Discrete, with Bound or Linear	`intlinprog`, Information	*	*	*	*

Note

This table does not list multiobjective solvers nor equation solvers. See Problems Handled by Optimization Toolbox Functions for a complete list of problems addressed by Optimization Toolbox functions.

Note

Some solvers have several algorithms. For help choosing, see Choosing the Algorithm.