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The following table describes fields in the optimization options structure options. You can set values of these fields using the function optimset. The column labeled L, M, B indicates whether the option applies to large-scale methods, medium scale methods, or both:
L — Large-scale methods only
M — Medium-scale methods only
B — Both large- and medium-scale methods
I — Interior-point method only
See the individual function reference pages for information about available option values and defaults.
The default values for the options vary depending on which optimization function you call with options as an input argument. You can determine the default option values for any of the optimization functions by entering optimset followed by the name of the function. For example,
optimset fmincon
returns a list of the options and the default values for fmincon. Options with default values listed as [] are either not used by the function, or have different default values depending on the algorithms the solver uses.
Optimization Options
| Option Name | Description | L, M, B, I | Used by Functions | |
|---|---|---|---|---|
| Algorithm | Chooses the algorithm used by the solver. | B, I | fmincon, fsolve, lsqcurvefit, lsqnonlin | |
| AlwaysHonorConstraints | The default 'bounds' ensures that bound constraints are satisfied at every iteration. Turn off by setting to 'none'. | I | fmincon | |
| BranchStrategy | Strategy bintprog uses to select branch variable. | M | ||
| DerivativeCheck | Compare user-supplied analytic derivatives (gradients or Jacobian, depending on the selected solver) to finite differencing derivatives. | B | fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin | |
| Diagnostics | Display diagnostic information about the function to be minimized or solved. | B | All but fminbnd, fminsearch, fzero, and lsqnonneg | |
DiffMaxChange | Maximum change in variables for finite differencing. | B, I | fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin | |
DiffMinChange | Minimum change in variables for finite differencing. | B, I | fgoalattain, fmincon, fminimax, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin | |
| Display | Level of display.
| B, I | All. See the individual function reference pages for the values that apply. | |
| FinDiffType | 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 AlwaysHonorConstraints option is set to 'none'. | M, I | ||
| FunValCheck | 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. | B | fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, lsqcurvefit, lsqnonlin | |
| GoalsExactAchieve | Specify the number of objectives required for the objective fun to equal the goal goal. Objectives should be partitioned into the first few elements of F. | M | ||
| GradConstr | User-defined gradients for the nonlinear constraints. | M, I | ||
| GradObj | User-defined gradients for the objective functions. | B | ||
| HessFcn | Function handle to a user-supplied Hessian (see Hessian). | I | fmincon | |
| Hessian | If 'user-supplied', function uses user-defined Hessian or Hessian information (when using HessMult), for the objective function. If 'off', function approximates the Hessian using finite differences. | L, I | ||
| HessMult | Handle to a user-supplied Hessian multiply function. Ignored unless Hessian is 'user-supplied' or 'on'. | L, I | ||
| HessPattern | 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. | L | ||
| HessUpdate | Quasi-Newton updating scheme. | M | ||
| InitBarrierParam | Initial barrier value. | I | fmincon | |
| InitialHessMatrix | Initial quasi-Newton matrix. | M | ||
| InitialHessType | Initial quasi-Newton matrix type. | M | ||
| InitTrustRegionRadius | Initial radius of the trust region. | I | fmincon | |
| Jacobian | If 'on', function uses user-defined Jacobian or Jacobian information (when using JacobMult), for the objective function. If 'off', function approximates the Jacobian using finite differences. | B | ||
| JacobMult | User-defined Jacobian multiply function. Ignored unless Jacobian is 'on' for fsolve, lsqcurvefit, and lsqnonlin. | L | ||
| JacobPattern | Sparsity pattern of the Jacobian for finite differencing. The size of the matrix is m-by-n, where m is 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. | L | ||
| LargeScale | Use large-scale algorithm if possible. | B | fminunc, fsolve, linprog, lsqcurvefit, lsqlin, lsqnonlin, quadprog | |
| LevenbergMarquardt | Choose Gauss-Newton algorithm by setting LevenbergMarquardt to 'off' and LargeScale to 'off'. | M | ||
| LineSearchType | Line search algorithm choice. | M | ||
| MaxFunEvals | Maximum number of function evaluations allowed. | B | fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, lsqcurvefit, lsqnonlin | |
| MaxIter | Maximum number of iterations allowed. | B | ||
| MaxNodes | Maximum number of possible solutions, or nodes, the binary integer programming function bintprog searches. | M | ||
| MaxPCGIter | Maximum number of iterations of preconditioned conjugate gradients method allowed. | L | fmincon, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog | |
| MaxProjCGIter | A tolerance for the number of projected conjugate gradient iterations; this is an inner iteration, not the number of iterations of the algorithm. | I | fmincon | |
| MaxRLPIter | Maximum number of iterations of linear programming relaxation method allowed. | M | ||
| MaxSQPIter | Maximum number of iterations of sequential quadratic programming method allowed. | M | ||
| MaxTime | Maximum amount of time in seconds allowed for the algorithm. | M | ||
| MeritFunction | Use goal attainment/minimax merit function (multiobjective) vs. fmincon (single objective). | M | ||
| MinAbsMax | Number of F(x) to minimize the worst case absolute values. | M | ||
| NodeDisplayInterval | Node display interval for bintprog. | M | ||
| NodeSearchStrategy | Search strategy that bintprog uses. | M | ||
| NonlEqnAlgorithm | Specify the Gauss-Newton algorithm for solving nonlinear equations by setting NonlEqnAlgorithm to 'gn' and LargeScale to 'off'. | M | ||
| ObjectiveLimit | If the objective function value goes below ObjectiveLimit and the iterate is feasible, then the iterations halt. | I | fmincon | |
| OutputFcn | Specify one or more user-defined functions that the optimization function calls at each iteration. See Output Function. | B | fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, lsqcurvefit, lsqnonlin | |
| PlotFcns | Plots various measures of progress while the algorithm executes, select from predefined plots or write your own.
See Plot Functions. | B | fgoalattain, fminbnd, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, fzero, lsqcurvefit, and lsqnonlin. See the individual function reference pages for the values that apply. | |
| PrecondBandWidth | Upper bandwidth of preconditioner for PCG. Setting to 'Inf' uses a direct factorization instead of CG. | L | fmincon, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog | |
| RelLineSrchBnd | Relative bound on line search step length. | M | ||
| RelLineSrchBndDuration | Number of iterations for which the bound specified in RelLineSrchBnd should be active. | M | ||
| ScaleProblem | For fmincon, the default 'obj-and-constr' causes the algorithm to normalize all constraints and the objective function. Disable by setting to 'none'. For the other solvers, when using the Algorithm option 'levenberg-marquardt', setting the ScaleProblem option to 'jacobian' sometimes helps the solver on badly-scaled problems. | L, I | fmincon, fsolve, lsqcurvefit, lsqnonlin | |
| Simplex | If 'on', function uses the simplex algorithm. | M | ||
| SubproblemAlgorithm | Determines how the iteration step is calculated. | I | fmincon | |
| TolCon | Termination tolerance on the constraint violation. | B | ||
| TolConSQP | Constraint violation tolerance for the inner SQP iteration. | M | fgoalattain, fmincon, fminimax, fseminf | |
| TolFun | Termination tolerance on the function value. | B | bintprog, fgoalattain, fmincon, fminimax, fminsearch, fminunc, fseminf, fsolve, linprog (L only), lsqcurvefit, lsqlin (L only), lsqnonlin, quadprog (L only) | |
| TolPCG | Termination tolerance on the PCG iteration. | L | fmincon, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog | |
| TolProjCG | A relative tolerance for projected conjugate gradient algorithm; this is for an inner iteration, not the algorithm iteration. | I | fmincon | |
| TolProjCGAbs | Absolute tolerance for projected conjugate gradient algorithm; this is for an inner iteration, not the algorithm iteration. | I | fmincon | |
| TolRLPFun | Termination tolerance on the function value of a linear programming relaxation problem. | M | ||
| TolX | Termination tolerance on x. | B | All functions except the medium-scale algorithms for linprog, lsqlin, and quadprog | |
| TolXInteger | Tolerance within which bintprog considers the value of a variable to be an integer. | M | ||
| TypicalX | 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. | B | fgoalattain, fmincon, fminimax, fminunc, fsolve, lsqcurvefit, lsqlin, lsqnonlin, quadprog | |
| UseParallel | When 'always', applicable solvers estimate gradients in parallel. Disable by setting to 'never'. | M, I |
The Outputfcn field of the options structure specifies one or more functions that an optimization function calls at each iteration. Typically, you might use an output function to plot points at each iteration or to display optimization quantities from the algorithm. Using an output function you can view, but not set, optimization quantities. To set up an output function, do the following:
Write the output function as an M-file function or subfunction.
Use optimset to set the value of Outputfcn to be a function handle, that is, the name of the function preceded by the @ sign. For example, if the output function is outfun.m, the command
options = optimset('OutputFcn', @outfun);specifies OutputFcn to be the handle to outfun. To specify more than one output function, use the syntax
options = optimset('OutputFcn',{@outfun, @outfun2});Call the optimization function with options as an input argument.
See Output Functions for an example of an output function.
Passing Extra Parameters explains how to parameterize the output function OutputFcn, if necessary.
The function definition line of the output function has the following form:
stop = outfun(x, optimValues, state)
where
x is the point computed by the algorithm at the current iteration.
optimValues is a structure containing data from the current iteration. Fields in optimValues describes the structure in detail.
state is the current state of the algorithm. States of the Algorithm lists the possible values.
stop is a flag that is true or false depending on whether the optimization routine should quit or continue. See Stop Flag for more information.
The optimization function passes the values of the input arguments to outfun at each iteration.
The following table lists the fields of the optimValues structure. A particular optimization function returns values for only some of these fields. For each field, the Returned by Functions column of the table lists the functions that return the field.
Corresponding Output Arguments. Some of the fields of optimValues correspond to output arguments of the optimization function. After the final iteration of the optimization algorithm, the value of such a field equals the corresponding output argument. For example, optimValues.fval corresponds to the output argument fval. So, if you call fmincon with an output function and return fval, the final value of optimValues.fval equals fval. The Description column of the following table indicates the fields that have a corresponding output argument.
Command-Line Display. The values of some fields of optimValues are displayed at the command line when you call the optimization function with the Display field of options set to 'iter', as described in Displaying Iterative Output. For example, optimValues.fval is displayed in the f(x) column. The Command-Line Display column of the following table indicates the fields that you can display at the command line.
In the following table, L, M, and B indicate:
L — Function returns a value to the field when using a large-scale algorithm.
M — Function returns a value to the field when using a medium-scale algorithm.
B — Function returns a value to the field when using both large- and medium-scale algorithms.
optimValues Fields
| OptimValues Field (optimValues.field) | Description | Returned by Functions | Command-Line Display |
|---|---|---|---|
attainfactor | Attainment factor for multiobjective problem. For details, see Goal Attainment Method. | fgoalattain (M) | None |
cgiterations | Number of conjugate gradient iterations at current optimization iteration. | fmincon (L), fsolve (L), lsqcurvefit (L), lsqnonlin (L) | CG-iterations |
constrviolation | Maximum constraint violation. | fgoalattain (M), fmincon (M), fminimax (M), fseminf (M) | max constraint |
degenerate | Measure of degeneracy. A point is degenerate if The partial derivative with respect to one of the variables is 0 at the point. A bound constraint is active for that variable at the point. See Degeneracy. | fmincon (L), fsolve (L), lsqcurvefit (L), lsqnonlin (L) | None |
directionalderivative | Directional derivative in the search direction. | fgoalattain (M), fmincon (M), fminimax (M), fminunc (M), fseminf (M), fsolve (M), lsqcurvefit (M), lsqnonlin (M) | Directional derivative |
firstorderopt | First-order optimality (depends on algorithm). Final value equals optimization function output output.firstorderopt. | fgoalattain (M), fmincon (B), fminimax (M), fminunc (M), fseminf (M), fsolve (B), lsqcurvefit (B), lsqnonlin (B) | First-order optimality |
funccount | Cumulative number of function evaluations. Final value equals optimization function output output.funcCount. | fgoalattain (M), fminbnd (B), fmincon (B), fminimax (M), fminsearch (B), fminunc (B), | F-count |
fval | Function value at current point. Final value equals optimization function output fval. | fgoalattain (M), fminbnd (B), fmincon (B), fminimax (M), fminsearch (B), fminunc (B), fseminf (M),
fsolve (B), | f(x) |
gradient | Current gradient of objective function — either analytic gradient if you provide it or finite-differencing approximation. Final value equals optimization function output grad. | fgoalattain (M), fmincon (B), fminimax (M), fminunc (M), fseminf (M), fsolve (B), lsqcurvefit (B), lsqnonlin (B) | None |
iteration | Iteration number — starts at 0. Final value equals optimization function output output.iterations. | fgoalattain (M), fminbnd (B),fmincon (B), fminimax (M), fminsearch (B), fminunc (B), fsolve (B), fseminf (M), fzero (B), lsqcurvefit (B), lsqnonlin (B) | Iteration |
lambda | The Levenberg-Marquardt parameter, lambda, at the current iteration. See Levenberg-Marquardt Method. | fsolve (B, Levenberg-Marquardt and Gauss-Newton algorithms), lsqcurvefit (B, Levenberg-Marquardt and Gauss-Newton algorithms), lsqnonlin (B, Levenberg-Marquardt and Gauss-Newton algorithms) | Lambda |
maxfval | Maximum function value | fminimax (M) | None |
positivedefinite | 0 if algorithm detects negative curvature while computing Newton step. 1 otherwise. | fmincon (L), fsolve (L), lsqcurvefit (L), lsqnonlin (L) | None |
procedure | Procedure messages. | fgoalattain (M), fminbnd (B), fmincon (M), fminimax (M), fminsearch (B), fseminf (M), | Procedure |
ratio | Ratio of change in the objective function to change in the quadratic approximation. | fmincon (L), fsolve (L), lsqcurvefit (L), lsqnonlin (L) | None |
residual | The residual vector. For fsolve, residual means the 2-norm of the residual squared. | lsqcurvefit (B), lsqnonlin (B), fsolve (B) | Residual |
resnorm | 2-norm of the residual squared. | lsqcurvefit (B), lsqnonlin (B) | Resnorm |
searchdirection | Search direction. | fgoalattain (M), fmincon (M), fminimax (M), fminunc (M), fseminf (M), fsolve (M), lsqcurvefit (M), lsqnonlin (M) | None |
stepaccept | Status of the current trust-region step. Returns true if the current trust-region step was successful, and false if the trust-region step was unsuccessful. | fsolve (L, NonlEqnAlgorithm='dogleg') | None |
stepsize | Current step size (displacement in x). Final value equals optimization function output output.stepsize. | fgoalattain (M), fmincon (B), fminimax (M), fminunc (B), fseminf (M), fsolve (B), lsqcurvefit (B), lsqnonlin (B) | Step-size or Norm of Step |
trustregionradius | Radius of trust region. | fmincon (L), fsolve (L, M), lsqcurvefit, lsqnonlin (L) | Trust-region radius |
Degeneracy. The value of the field degenerate, which measures the degeneracy of the current optimization point x, is defined as follows. First, define a vector r, of the same size as x, for which r(i) is the minimum distance from x(i) to the ith entries of the lower and upper bounds, lb and ub. That is,
r = min(abs(ub-x, x-lb))
Then the value of degenerate is the minimum entry of the vector r + abs(grad), where grad is the gradient of the objective function. The value of degenerate is 0 if there is an index i for which both of the following are true:
grad(i) = 0
x(i) equals the ith entry of either the lower or upper bound.
The following table lists the possible values for state:
| State | Description |
|---|---|
'init' | The algorithm is in the initial state before the first iteration. |
'interrupt' | The algorithm is in some computationally expensive part of the iteration. In this state, the output function can interrupt the current iteration of the optimization. At this time, the values of x and optimValues are the same as at the last call to the output function in which state=='iter'. |
'iter' | The algorithm is at the end of an iteration. |
'done' | The algorithm is in the final state after the last iteration. |
The following code illustrates how the output function might use the value of state to decide which tasks to perform at the current iteration:
switch state
case 'iter'
% Make updates to plot or guis as needed
case 'interrupt'
% Probably no action here. Check conditions to see
% whether optimization should quit.
case 'init'
% Setup for plots or guis
case 'done'
% Cleanup of plots, guis, or final plot
otherwise
endThe output argument stop is a flag that is true or false. The flag tells the optimization function whether the optimization should quit or continue. The following examples show typical ways to use the stop flag.
Stopping an Optimization Based on Data in optimValues. The output function can stop an optimization at any iteration based on the current data in optimValues. For example, the following code sets stop to true if the directional derivative is less than .01:
function stop = outfun(x, optimValues)
stop = false;
% Check if directional derivative is less than .01.
if optimValues.directionalderivative < .01
stop = true;
end Stopping an Optimization Based on GUI Input. If you design a GUI to perform optimizations, you can make the output function stop an optimization when a user clicks a Stop button on the GUI. The following code shows how to do this, assuming that the Stop button callback stores the value true in the optimstop field of a handles structure called hObject:
function stop = outfun(x) stop = false; % Check if user has requested to stop the optimization. stop = getappdata(hObject,'optimstop');
The PlotFcns field of the options structure specifies one or more functions that an optimization function calls at each iteration to plot various measures of progress while the algorithm executes. The structure of a plot function is the same as that for an output function. For more information on writing and calling a plot function, see Output Function.
To view and modify a predefined plot function listed for PlotFcns in Optimization Options, you can open it in the MATLAB Editor. For example, to view the M-file corresponding to the norm of residuals, type:
edit optimplotresnorm.m
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