Nonnegative real. intlinprog stops if the difference between the internally calculated upper (U) and lower (L) bounds on the objective function is less than or equal to AbsoluteGapTolerance:

U – L <= AbsoluteGapTolerance.

Number of F(x) to minimize the worst case absolute values.

fminimax

Chooses the algorithm used by the solver.

Rule for choosing the component for branching:

Compare user-supplied analytic derivatives (gradients or Jacobian, depending on the selected solver) to finite differencing derivatives.

fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Tolerance on the constraint violation.

fgoalattain, fmincon, fminimax, fseminf, intlinprog, linprog, lsqlin, quadprog

Level of cut generation (see Cut Generation):

Level of display.

All. See the individual function reference pages for the values that apply.

Specify the number of objectives required for the objective fun to equal the set goal. Reorder your objectives, if necessary, to have fgoalattain achieve the first EqualityGoalCount objectives exactly.

fgoalattain

Scalar or vector step size factor for finite differences. When you set FiniteDifferenceStepSize to a vector v, forward finite differences steps delta are

where sign′(x) = sign(x) except sign′(0) = 1. Central finite differences are

Scalar FiniteDifferenceStepSizeexpands to a vector. The default is sqrt(eps) for forward finite differences, and eps^(1/3) for central finite differences.

fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Finite differences, used to estimate gradients, are either 'forward' (the default), or 'central' (centered), which takes twice as many function evaluations but should be more accurate. 'central'differences might violate bounds during their evaluation in fmincon interior-point evaluations if the HonorBounds option is set to false.

fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Termination tolerance on the function value.

fgoalattain, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog

Method of Hessian approximation: 'bfgs', 'lbfgs', {'lbfgs',Positive Integer}, or 'finite-difference'.

Ignored when HessianFcn or HessianMultiplyFcn is nonempty.

fmincon

Function handle to a user-supplied Hessian (see Including Hessians).

Handle to a user-supplied Hessian multiply function.

Ignored when HessianFcn is nonempty.

fmincon, fminunc, quadprog

Algorithm for searching for feasible points (see Heuristics for Finding Feasible Solutions):

The default true ensures that bound constraints are satisfied at every iteration. Turn off by setting to false.

Types of integer preprocessing (see Mixed-Integer Program Preprocessing):

User-defined Jacobian multiply function. Ignored unless SpecifyObjectiveGradient is true for fsolve, lsqcurvefit, and lsqnonlin.

fsolve, lsqcurvefit, lsqlin, lsqnonlin

Maximum number of function evaluations allowed.

fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Maximum number of iterations allowed.

All but fzero and lsqnonneg

intlinprog

Maximum amount of time in seconds allowed for the algorithm.

intlinprog, linprog

Choose the node to explore next.

If the objective function value goes below ObjectiveLimit and the iterate is feasible, then the iterations halt.

Termination tolerance on the first-order optimality.

fgoalattain, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, linprog (interior-pointonly), lsqcurvefit, lsqlin, lsqnonlin, quadprog

Specify one or more user-defined functions that the optimization function calls at each iteration. See Output Function or intlinprog Output Functions and Plot Functions.

fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, intlinprog, lsqcurvefit, lsqnonlin

Plots various measures of progress while the algorithm executes. Select from predefined plots or write your own.

See Plot Functions or intlinprog Output Functions and Plot Functions.

fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, intlinprog, lsqcurvefit, lsqnonlin. See the individual function reference pages for the values that apply.

Real from 0 through 1. intlinprog stops if the relative difference between the internally calculated upper (U) and lower (L) bounds on the objective function is less than or equal toRelativeGapTolerance:

(U – L) / (abs(U) + 1) <= RelativeGapTolerance.

intlinprog automatically modifies the tolerance for large L magnitudes:

tolerance = min(1/(1+|L|), RelativeGapTolerance)

Algorithm for solving linear programs:

For fmincon interior-point and sqpalgorithms, true causes the algorithm to normalize all constraints and the objective function by their initial values. Disable by setting to the default false.

Simplex

Use Algorithm instead

If 'on', function uses the simplex algorithm.

linprog

User-defined gradients for the nonlinear constraints.

fgoalattain, fmincon, fminimax

User-defined gradients or Jacobians for the objective functions.

fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Termination tolerance on x.

All functions except linprogand lsqlin, and the quadprog'active-set' algorithm

Determines how the iteration step is calculated.

Array that specifies typical magnitude of array of parameters x. The size of the array is equal to the size of x0, the starting point. Primarily for scaling finite differences for gradient estimation.

fgoalattain, fmincon, fminimax, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog

When true, applicable solvers estimate gradients in parallel. Disable by setting to false.

fgoalattain, fmincon, fminimax, fminunc, fsolve, lsqcurvefit, lsqnonlin.

Display diagnostic information about the function to be minimized or solved.

All but fminbnd, fminsearch, fzero, and lsqnonneg

Maximum change in variables for finite differencing.

fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Minimum change in variables for finite differencing.

fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin

Check whether objective function and constraints values are valid. 'on' displays an error when the objective function or constraints return a value that is complex, NaN, or Inf.

'off' displays no error.

fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, lsqcurvefit, lsqnonlin

Sparsity pattern of the Hessian for finite differencing. The size of the matrix is n-by-n, where n is the number of elements in x0, the starting point.

fmincon, fminunc

Quasi-Newton updating scheme.

fminunc

Initial barrier value.

Initial Levenberg-Marquardt parameter.

Initial radius of the trust region.

Sparsity pattern of the Jacobian for finite differencing. The size of the matrix is m-by-n, where mis the number of values in the first argument returned by the user-specified function fun, and n is the number of elements in x0, the starting point.

fsolve, lsqcurvefit, lsqnonlin

Type of preprocessing for the solution to the relaxed linear program (see Linear Program Preprocessing):

Maximum number of iterations of preconditioned conjugate gradients method allowed.

fmincon, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog

A tolerance for the number of projected conjugate gradient iterations; this is an inner iteration, not the number of iterations of the algorithm.

Maximum number of iterations of sequential quadratic programming method allowed.

fgoalattain, fmincon, fminimax

Use goal attainment/minimax merit function (multiobjective) vs. fmincon (single objective).

fgoalattain, fminimax

Upper bandwidth of preconditioner for PCG. Setting to 'Inf' uses a direct factorization instead of CG.

fmincon, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog

Level of LP preprocessing prior to simplex or dual simplex algorithm iterations.

linprog

Relative bound on line search step length.

fgoalattain, fmincon, fminimax, fseminf

Number of iterations for which the bound specified in RelLineSrchBnd should be active.

fgoalattain, fmincon, fminimax, fseminf

When using the Algorithmoption 'levenberg-marquardt', setting the ScaleProblem option to 'jacobian' sometimes helps the solver on badly-scaled problems.

Constraint violation tolerance for the inner SQP iteration.

Termination tolerance on the PCG iteration.

fmincon, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog

A relative tolerance for projected conjugate gradient algorithm; this is for an inner iteration, not the algorithm iteration.

Absolute tolerance for projected conjugate gradient algorithm; this is for an inner iteration, not the algorithm iteration.

patternsearch

patternsearch

patternsearch

particleswarm, simulannealbnd

particleswarm

HybridInterval

simulannealbnd

ga, patternsearch

patternsearch

patternsearch

MigrationDirection

ga

MigrationFraction

ga

MigrationInterval

ga

PenaltyFactor

ga, patternsearch

PlotInterval

ga, patternsearch, simulannealbnd

StallTest

ga