Optimization Toolbox

Output Headings: Medium-Scale Algorithms

When the options Display parameter is set to 'iter' for fminsearch, fminbnd, fzero, fgoalattain, fmincon, lsqcurvefit, fminunc, fsolve, lsqnonlin, fminimax, and fseminf, output is produced in column format.

fminsearch

For fminsearch the column headings are

Iteration   Func-count     min f(x)         Procedure

where:

• Iteration is the iteration number.
• Func-count is the number of function evaluations.
• min f(x) is the minimum function value in the current simplex.
• Procedure gives the current simplex operation: initial, expand, reflect, shrink, contract inside and contract outside.

fzero and fminbnd

For fzero and fminbnd the column headings are

Func-count      x           f(x)         Procedure

where:

• Func-count is the number of function evaluations (which for fzero is the same as the number of iterations).
• x is the current point.
• f(x) is the current function value at x.
• Procedure gives the current operation. For fzero these include initial (initial point), search (search for a interval containing a zero), bisection (bisection search), and interpolation. For fminbnd, the possible operations are initial, golden (golden section search), and parabolic (parabolic interpolation).

fminunc

For fminunc, the column headings are

                                                    Directional
Iteration  Func-count     f(x)         Step-size     derivative

where:

• Iteration is the iteration number.
• Func-count is the number of function evaluations.
• f(x) is the current function value.
• Step-size is the step-size in the current search direction.
• Directional derivative is the gradient of the function along the search direction.

fsolve, lsqnonlin, and lsqcurvefit

For fsolve, lsqnonlin, and lsqcurvefit the headings are

                                             Directional 
Iteration  Func-count  Residual  Step-size   derivative   Lambda

where Iteration, Func-count, Step-size, and Directional derivative are the same as for fminunc, and:

• Residual is the residual (sum-of-squares) of the function.
• Lambda is the value defined in Least Squares Optimization. (This value is printed when the Levenberg-Marquardt method is used and omitted when the Gauss-Newton method is used.)

fmincon and fseminf

For fmincon and fseminf the headings are

                       max                  Directional 
Iter  F-count  f(x)  constraint  Step-size  derivative  Procedure

where:

• Iter is the iteration number.
• F-count is the number of function evaluations.
• f(x) is the current function value.
• max constraint is the maximum constraint violation.
• Step-size is the step-size in the search direction.
• Directional derivative is the gradient of the function along the search direction.
• Procedure gives a messages about the Hessian update and QP subproblem.

The Procedure messages are discussed in Updating the Hessian Matrix.

For fgoalattain and fminimax, the headings are the same as for fmincon except f(x) and max constraint are combined into Max{F,constraints}. Max{F,constraints} gives the maximum goal violation or constraint violation for fgoalattain, and the maximum function value or constraint violation for fminimax.

Displaying Iterative Output

Output Headings: Large-Scale Algorithms