## Exit Flags and Exit Messages

### Exit Flags

When an optimization solver completes its task, it sets an *exit
flag*. An exit flag is an integer that is a code for the reason the
solver halted its iterations. In general:

Positive exit flags correspond to successful outcomes.

Negative exit flags correspond to unsuccessful outcomes.

The zero exit flag corresponds to the solver being halted by exceeding an iteration limit or limit on the number of function evaluations (see Iterations and Function Counts, and also see Tolerances and Stopping Criteria).

This table links to the exit flag description of each solver.

**Exit Flags by Solver**

**Note**

Exit flags are not infallible guides to the quality of a solution. Many other factors, such as tolerance settings, can affect whether a solution is satisfactory to you. You are responsible for deciding whether a solver returns a satisfactory answer. Sometimes a negative exit flag does not correspond to a “bad” solution. Similarly, sometimes a positive exit flag does not correspond to a “good” solution.

You obtain an exit flag by calling a solver with the `exitflag`

syntax. This syntax depends on the solver. For details, see the solver function
reference pages. For example, for `fsolve`

, the calling syntax to obtain an exit flag is

[x,fval,exitflag] = fsolve(...)

The following example uses this syntax. Suppose you want to solve the system of nonlinear equations

$$\begin{array}{c}2{x}_{1}-{x}_{2}={e}^{-{x}_{1}}\\ -{x}_{1}+2{x}_{2}={e}^{-{x}_{2}}.\end{array}$$

Write these equations as an anonymous function that gives a zero vector at a solution:

myfcn = @(x)[2*x(1) - x(2) - exp(-x(1)); -x(1) + 2*x(2) - exp(-x(2))];

Call `fsolve`

with the `exitflag`

syntax at
the initial point [-5 -5]:

[xfinal fval exitflag] = fsolve(myfcn,[-5 -5])

Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. xfinal = 0.5671 0.5671 fval = 1.0e-06 * -0.4059 -0.4059 exitflag = 1

In the table for the `fsolve`

`exitflag`

, you find that an
exit flag value `1`

means “Function converged to a solution
`x`

.” In other words, `fsolve`

reports `myfcn`

is nearly zero at
`x`

= `[0.5671 0.5671]`

.

### Exit Messages

Each solver issues a message to the MATLAB^{®} command window
at the end of its iterations. This message explains briefly why the
solver halted. The message might give more detail than the exit flag.

Many examples in this documentation show exit messages, such as Define and Solve Problem at Command Line. The example in the previous section, Exit Flags, shows the following exit message:

Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient.

This message is more informative than the exit flag. The message
indicates that the gradient is relevant. The message also states that
the function tolerance controls how near 0 the vector of function
values must be for `fsolve`

to regard the solution
as completed.

### Enhanced Exit Messages

Some solvers have exit messages that contain links for more information. There are two types of links:

Links on words or phrases. These links give definitions of terms or other information.

A link as the last line of the display saying

`<stopping criteria details>`

. If you click this link, MATLAB displays more detail about the reason the solver halted.

The `fminunc`

solver has enhanced exit messages.

[xfinal fval exitflag] = fminunc(@sin,0)

This yields the following results:

Each of the underlined words or phrases contains a link that provides more information.

The

`<stopping criteria details>`

link prints the following to the MATLAB command line:Optimization completed: The first-order optimality measure, 0.000000e+00, is less than options.OptimalityTolerance = 1.000000e-06.

The other links point to the documentation for term definitions. For example, clicking the

`Local minimum found`

link opens the following:Clicking the

`first-order optimality measure`

link brings up the definition of first-order optimality measure for`fminunc`

:The other links lead to similar documentation definitions.

### Exit Message Options

Set the `Display`

option to control the appearance
of both exit messages and iterative display. For more information,
see Iterative Display. The
following table shows the effect of the various settings of the `Display`

option.

Value of the Display Option | Output to Command Window | |
---|---|---|

Exit message | Iterative Display | |

`'none'` , or the synonymous `'off'` | None | None |

`'final'` (default for most solvers) | Default | None |

`'final-detailed'` | Detailed | None |

`'iter'` | Default | Yes |

`'iter-detailed'` | Detailed | Yes |

`'notify'` | Default only if `exitflag` ≤ 0 | None |

`'notify-detailed'` | Detailed only if `exitflag` ≤ 0 | None |

For example,

opts = optimoptions(@fminunc,'Display','iter-detailed','Algorithm','quasi-newton'); [xfinal fval] = fminunc(@cos,1,opts);

yields the following display: