Documentation

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

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

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

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

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

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

linprog, quadprog

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

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

fgoalattain

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

quadprog

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

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

The number of semi-infinite constraints.

fseminf

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

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

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

fgoalattain

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

lsqcurvefit

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

The interval over which the function is minimized.

fminbnd

The attainment factor at the solution x.

fgoalattain

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

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

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

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

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 the quasi-newton, active-set, or sqp methods, hessian is the value of the Quasi-Newton approximation to the Hessian at the solution x. See Hessian.

fmincon, fminunc

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

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

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

fminimax

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

The value of the residual at the solution x.

lsqcurvefit, lsqlin, lsqnonlin, lsqnonneg

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

lsqcurvefit, lsqlin, lsqnonlin, lsqnonneg

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