Iteration or Iter

Iteration number; see Iterations and Function Counts

Func-count or F-count

Number of function evaluations; see Iterations and Function Counts

x

Current point for the algorithm

f(x)

Current function value

Step-size

Step size in the current search direction

Norm of step

Norm of the current step

Explored nodes

Cumulative number of explored nodes

Obj of LP relaxation

Objective function value of the linear programming (LP) relaxation problem

Obj of best integer point

Objective function value of the best integer point found so far. This is an upper bound for the final objective function value.

Unexplored nodes

Number of nodes that have been set up but not yet explored

Best lower bound on obj

Objective function value of LP relaxation problem that gives the best current lower bound on the final objective function value

Relative gap between bounds

where

• b is the objective function value of the best integer point.

• a is the best lower bound on the objective function value.

min f(x)

Minimum function value in the current simplex

Procedure

Simplex procedure at the current iteration. Procedures include initial, expand, reflect, shrink, contract inside, and contract outside. See fminsearch Algorithm for explanations of these procedures.

Procedure

Procedure at the current operation. Procedures for fzero:

• initial (initial point)

• search (search for an interval containing a zero)

• bisection (bisection search)

• interpolation

Operations for fminbnd:

• initial

• golden (golden section search)

• parabolic (parabolic interpolation)

First-order optimality

First-order optimality measure (see First-Order Optimality Measure)

CG-iterations

Number of conjugate gradient iterations taken by the current (optimization) iteration (see Preconditioned Conjugate Gradient Method)

First-order optimality

First-order optimality measure (see First-Order Optimality Measure)

Trust-region radius

Current trust-region radius (change in the norm of the trust-region radius)

Residual

Residual (sum of squares) of the function

Directional derivative

Gradient of the function along the search direction

Max constraint

Maximum violation among all constraints, both internally constructed and user-provided

First-order optimality

First-order optimality measure (see First-Order Optimality Measure)

CG-iterations

Number of conjugate gradient iterations taken by the current (optimization) iteration (see Preconditioned Conjugate Gradient Method)

Trust-region radius

Current trust-region radius

Residual

Residual (sum of squares) of the function

Attainment factor

Value of the attainment factor for fgoalattain

Objective value

Objective function value of the nonlinear programming reformulation of the minimax problem for fminimax

Directional derivative

Current gradient of the function along the search direction

Procedure

Hessian update and QP subproblem. The Procedure messages are discussed in Updating the Hessian Matrix.

Primal Infeas A*x-b

Primal infeasibility

Dual Infeas A'*y+z-w-f

Dual infeasibility

Duality Gap x'*z+s'*w

Duality gap (see Large Scale Linear Programming) between the primal objective and the dual objective. s and w appear only in this equation if there are finite upper bounds.

Total Rel Error

Total relative error, described at the end of Main Algorithm.

Objective f'*x

Current objective value

Resnorm

Value of the squared 2-norm of the residual at x

Residual

Residual vector of the function

First-order optimality

First-order optimality measure (see First-Order Optimality Measure)

CG-iterations

Number of conjugate gradient iterations taken by the current (optimization) iteration (see Preconditioned Conjugate Gradient Method)

Directional derivative

Gradient of the function along the search direction

Lambda

λ_k value defined in Levenberg-Marquardt Method. (This value is displayed when you use the Levenberg-Marquardt method and omitted when you use the Gauss-Newton method.)