Optimization Toolbox

Output Headings: Large-Scale Algorithms

fminunc

For fminunc, the column headings are

                       Norm of     First-order
Iteration      f(x)      step      optimality     CG-iterations

where:

• Iteration is the iteration number.
• f(x) is the current function value.
• Norm of step is the norm of the current step-size.
• First-order optimality is the infinity norm of the current gradient.
• CG-iterations is the number of iterations taken by PCG (see Preconditioned Conjugate Gradients) at the current (optimization) iteration.

lsqnonlin, lsqcurvefit, and fsolve

For lsqnonlin, lsqcurvefit, and fsolve the column headings are

                             Norm of   First-order 
Iteration  Func-count  f(x)   step     optimality   CG-iterations

where:

• Iteration is the iteration number.
• Func-count is the number of function evaluations.
• f(x) is the sum-of-the-squares of the current function values.
• Norm of step is the norm of the current step-size.
• First-order optimality is a measure of first-order optimality. For bound constrained problems, the first-order optimality is the infinity norm of v.*g, where v is defined as in Box Constraints and g is the gradient. For unconstrained problems, it is the infinity norm of the current gradient.
• CG-iterations is the number of iterations taken by PCG (see Preconditioned Conjugate Gradients) at the current (optimization) iteration.

fmincon

For fmincon, the column headings are

                        Norm of     First-order
Iteration     f(x)       step       optimality     CG-iterations

where:

• Iteration is the iteration number.
• f(x) is the current function value.
• Norm of step is the norm of the current step-size.
• First-order optimality is a measure of first-order optimality. For bound constrained problems, the first-order optimality is the infinity norm of v.*g, where v is defined as in Box Constraints and g is the gradient. For equality constrained problems, it is the infinity norm of the projected gradient. (The projected gradient is the gradient projected into the nullspace of Aeq.)
• CG-iterations is the number of iterations taken by PCG (see Preconditioned Conjugate Gradients) at the current (optimization) iteration.

linprog

For linprog the column headings are

Residuals:   Primal     Dual      Upper     Duality      Total
             Infeas    Infeas     Bounds      Gap         Rel
             A*x-b   A'*y+z-w-f  {x}+s-ub   x'*z+s'*w    Error

where:

• Primal Infeas A*x-b is the norm of the residual A*x - b.
• Dual Infeas A'*y+z-w-f is the norm of the residual A'*y+z-w-f (where w is all zero if there are no finite upper bounds).
• Upper Bounds {x}+s-ub is the norm of the residual spones(s).*x+s-ub (which is defined to be zero if all variables are unbounded above). This column is not printed if no finite upper bounds exist.
• Duality Gap x'*z+s'*w is the duality gap (see Large-Scale Linear Programming) between the primal objective and the dual objective. s and w only appear in this equation if there are finite upper bounds.
• Total Rel Error is the total relative error described at the end of the Main Algorithm subsection of Large-Scale Linear Programming.

Output Headings: Medium-Scale Algorithms

Optimization of Inline Objects Instead of M-Files