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Function Arguments

Input Arguments

Argument

Description

Used by Functions

A, b

The matrix A and vector b are, respectively, the coefficients of the linear inequality constraints and the corresponding right-side vector: A*x ≤ b.

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

Aeq, beq

The matrix Aeq and vector beq are, respectively, the coefficients of the linear equality constraints and the corresponding right-side vector: Aeq*x = beq.

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

C, d

The matrix C and vector d are, respectively, the coefficients of the over or underdetermined linear system and the right-side vector to be solved.

lsqlin, lsqnonneg

f

The vector of coefficients for the linear term in the linear equation f'*x or the quadratic equation x'*H*x+f'*x.

bintprog, linprog, quadprog

fun

The function to be optimized. fun is either a function handle to a file or is an anonymous function. See the individual function reference pages for more information on fun.

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

goal

Vector of values that the objectives attempt to attain. The vector is the same length as the number of objectives.

fgoalattain

H

The matrix of coefficients for the quadratic terms in the quadratic equation x'*H*x+f'*x. H must be symmetric.

quadprog

lb, ub

Lower and upper bound vectors (or matrices). The arguments are normally the same size as x. However, if lb has fewer elements than x, say only m, then only the first m elements in x are bounded below; upper bounds in ub can be defined in the same manner. You can also specify unbounded variables using -Inf (for lower bounds) or Inf (for upper bounds). For example, if lb(i) = -Inf, the variable x(i) is unbounded below.

fgoalattain, fmincon, fminimax, fseminf, linprog, lsqcurvefit, lsqlin, lsqnonlin, quadprog

nonlcon

The function that computes the nonlinear inequality and equality constraints. Passing Extra Parameters explains how to parameterize the function nonlcon, if necessary.

See the individual reference pages for more information on nonlcon.

fgoalattain, fmincon, fminimax

ntheta

The number of semi-infinite constraints.

fseminf

options

A structure that defines options used by the optimization functions. For information about the options, see Optimization Options Reference or the individual function reference pages.

All functions

seminfcon

The function that computes the nonlinear inequality and equality constraints and the semi-infinite constraints. seminfcon is the name of a function file or MEX-file. Passing Extra Parameters explains how to parameterize seminfcon, if necessary.

See the function reference pages for fseminf for more information on seminfcon.

fseminf

weight

A weighting vector to control the relative underattainment or overattainment of the objectives.

fgoalattain

xdata, ydata

The input data xdata and the observed output data ydata that are to be fitted to an equation.

lsqcurvefit

x0

Starting point (a scalar, vector or matrix).

(For fzero, x0 can also be a two-element vector representing a finite interval that is known to contain a zero.)

All functions except fminbnd

x1, x2

The interval over which the function is minimized.

fminbnd

Output Arguments

ArgumentDescriptionUsed by Functions
attainfactor

The attainment factor at the solution x.

fgoalattain

exitflag

An integer identifying the reason the optimization algorithm terminated. See the function reference pages for descriptions of exitflag specific to each function, and Exit Flags and Exit Messages.

You can also return a message stating why an optimization terminated by calling the optimization function with the output argument output and then displaying output.message.

All functions

fval

The value of the objective function fun at the solution x.

bintprog, fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, linprog, quadprog

grad

The value of the gradient of fun at the solution x. If fun does not compute the gradient, grad is a finite-differencing approximation of the gradient.

fmincon, fminunc

hessian

The value of the Hessian of fun at the solution x. For large-scale methods, if fun does not compute the Hessian, hessian is a finite-differencing approximation of the Hessian. For medium-scale methods, hessian is the value of the Quasi-Newton approximation to the Hessian at the solution x. See Hessian.

fmincon, fminunc

jacobian

The value of the Jacobian of fun at the solution x. If fun does not compute the Jacobian, jacobian is a finite-differencing approximation of the Jacobian.

lsqcurvefit, lsqnonlin, fsolve

lambda

The Lagrange multipliers at the solution x, see Lagrange Multiplier Structures. lambda is a structure where each field is for a different constraint type. For structure field names, see individual function descriptions. (For lsqnonneg, lambda is simply a vector, as lsqnonneg only handles one kind of constraint.)

fgoalattain, fmincon, fminimax, fseminf, linprog, lsqcurvefit, lsqlin, lsqnonlin, lsqnonneg, quadprog

maxfval

max{fun(x)} at the solution x.

fminimax

output

An output structure that contains information about the results of the optimization, see Output Structures. For structure field names, see individual function descriptions.

All functions

residual

The value of the residual at the solution x.

lsqcurvefit, lsqlin, lsqnonlin, lsqnonneg

resnorm

The value of the squared 2-norm of the residual at the solution x.

lsqcurvefit, lsqlin, lsqnonlin, lsqnonneg

x

The solution found by the optimization function. If exitflag > 0, then x is a solution; otherwise, x is the value of the optimization routine when it terminated prematurely.

All functions

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