Iterative display is a table of statistics describing the calculations in each iteration of a solver. The statistics depend on both the solver and the solver algorithm. For more information about iterations, see Iterations and Function Counts. The table appears in the MATLAB^{®} Command Window when you run solvers with appropriate options.
Obtain iterative display by using optimoptions
to
create options with the Display
option set to 'iter'
or 'iterdetailed'
.
For example:
options = optimoptions(@fminunc,'Display','iter','Algorithm','quasinewton'); [x fval exitflag output] = fminunc(@sin,0,options); Firstorder Iteration Funccount f(x) Stepsize optimality 0 2 0 1 1 4 0.841471 1 0.54 2 8 1 0.484797 0.000993 3 10 1 1 5.62e005 4 12 1 1 0 Local minimum found. Optimization completed because the size of the gradient is less than the default value of the function tolerance.
You can also obtain iterative display by using the Optimization
app. Select Display to command window > Level of display
> iterative
or iterative
with detailed message
.
Iterative display is available for all solvers except:
lsqlin
'trustregionreflective'
and 'activeset'
algorithms
lsqnonneg
quadprog
'trustregionreflective'
algorithm
The following table lists some common headings of iterative display.
Heading  Information Displayed 

 Current objective function value. For 
 Firstorder optimality measure (see FirstOrder Optimality Measure). 
 Number of function evaluations; see Iterations and Function Counts. 
 Iteration number; see Iterations and Function Counts. 
 Size of the current step (size is the Euclidean norm,
or 2norm). For the 
The following sections describe headings of iterative display whose meaning is specific to the optimization function you are using:
The following table describes the headings specific to fgoalattain
, fmincon
, fminimax
, and fseminf
.
fgoalattain, fmincon, fminimax, or fseminf Heading  Information Displayed 

 Value of the attainment factor for 
 Number of conjugate gradient iterations taken in the current iteration (see Preconditioned Conjugate Gradient Method). 
 Gradient of the objective function along the search direction. 
 Maximum constraint violation, where satisfied inequality
constraints count as 
 Multiplicative factor that scales the search direction (see Equation 645). 
 Maximum violation among all constraints, both internally constructed and userprovided; can be negative when no constraint is binding. 
 Objective function value of the nonlinear programming
reformulation of the minimax problem for 
 Hessian update procedures:
For more information, see Updating the Hessian Matrix. QP subproblem procedures:

 Multiplicative factor that scales the search direction (see Equation 645). 
 Current trustregion radius. 
The following table describes the headings specific to fminbnd
and fzero
.
fminbnd or fzero Heading  Information Displayed 

 Procedures for
Procedures for

 Current point for the algorithm 
The following table describes the headings specific to fminsearch
.
fminsearch Heading  Information Displayed 

 Minimum function value in the current simplex. 
 Simplex procedure at the current iteration. Procedures include:
For details, see 
The following table describes the headings specific to fminunc
.
fminunc Heading  Information Displayed 

 Number of conjugate gradient iterations taken in the current iteration (see Preconditioned Conjugate Gradient Method) 
 Multiplicative factor that scales the search direction (see Equation 611) 
The fminunc
'quasinewton'
algorithm
can issue a skipped update
message to the right
of the Firstorder optimality
column. This message
means that fminunc
did not update its Hessian
estimate, because the resulting matrix would not have been positive
definite. The message usually indicates that the objective function
is not smooth at the current point.
The following table describes the headings specific to fsolve
.
fsolve Heading  Information Displayed 

 Gradient of the function along the search direction 
 λ_{k} value defined in LevenbergMarquardt Method 
 Residual (sum of squares) of the function 
 Current trustregion radius (change in the norm of the trustregion radius) 
The following table describes the headings specific to intlinprog
.
intlinprog Heading  Information Displayed  

 Cumulative number of explored nodes.  
 Time in seconds since  
 Number of integer feasible points found.  
 Objective function value of the best integer feasible point found. This is an upper bound for the final objective function value.  
 $$\frac{100(ba)}{\leftb\right+1},$$ where

The following table describes the headings specific to linprog
. Each algorithm has its own iterative
display.
linprog Heading  Information Displayed 

 Primal infeasibility, a measure of the constraint violations, which should be zero at a solution. For definitions, see PredictorCorrector ( 
 Dual infeasibility, a measure of the derivative of the Lagrangian, which should be zero at a solution. For the
definition of the Lagrangian, see PredictorCorrector. For the definition of dual infeasibility,
see PredictorCorrector ( 
 Upper bound feasibility. {x} means those x with finite upper bounds. This is the r_{u} residual in InteriorPointLegacy Linear Programming. 
 Duality gap (see InteriorPointLegacy Linear Programming) between the primal objective
and the dual objective. 
 Total relative error, described at the end of Main Algorithm. 
 A measure of the Lagrange multipliers times distance from the bounds, which should be zero at a solution. See the r_{c} variable in Stopping Conditions. 
 Time in seconds that 
The lsqlin
'interiorpoint'
iterative
display is inherited from the quadprog
iterative
display. The relationship between these functions is explained in InteriorPoint Linear Least Squares. For
iterative display details, see quadprog.
The following table describes the headings specific to lsqnonlin
and lsqcurvefit
.
lsqnonlin or lsqcurvefit Heading  Information Displayed 

 Gradient of the function along the search direction 
 λ_{k} value defined in LevenbergMarquardt Method 
 Value of the squared 2norm of the residual at 
 Residual vector of the function 
The following table describes the headings specific to quadprog
. Only the 'interiorpointconvex'
algorithm
has iterative display.
quadprog Heading  Information Displayed 

 Primal infeasibility, defined as 
 Dual infeasibility, defined as 
 A measure of the maximum absolute value of the Lagrange multipliers of inactive inequalities, which should be zero at a solution. This quantity is g in Infeasibility Detection. 