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迭代显示

介绍

The iterative display is a table of statistics describing the calculations in each iteration of a solver. The statistics depend on both the solver and the solver algorithm. The table appears in the MATLAB^®Command Window when you run solvers with appropriate options. For more information about iterations, see迭代ations and Function Counts。

通过使用optimoptions与Displayoption set to'iter'或者'iTer-detailed'。For example:

options = optimoptions（@fminunc，'display'，'iter'，'算法'，'quasi-newton'）;[x fval Exitflag输出] = fminunc（@sin，0，options）;

一阶迭代func -count f（x）阶梯尺寸最优性0 2 0 1 1 1 4 -0.841471 1 0.54 2 8 -1 0.484797 0.000993 3 10 -1 1 5.62E -05 4 12 -1 1 1 0局部最小值。完成优化是因为梯度的大小小于最佳公差的值。

The iterative display is available for all solvers except:

lsqlin“信任区域反射”算法
LSQNONNEG
Quadprog“信任区域反射”算法

通用标题

This table lists some common headings of iterative display.

标题	显示的信息
`f(x)`或者`FVAL`	当前的目标函数值；为了`FSOLVE`, the square of the norm of the function value vector
`一阶最优性`	一阶最优性measure (see一阶最佳度量)
`功能计数`或者`F计数`	功能评估次数；看迭代ations and Function Counts
`迭代ation`或者`迭代`	迭代编号；看迭代ations and Function Counts
`Norm of step`	当前步骤的大小（大小是欧几里得规范，或2个norm）。为了`“信任区”`和`“信任区域反射”`算法s, when constraints exist,`Norm of step`is the norm of`D*s`。这里，`s`是步骤和`D`是算法描述的“信任区”子问题部分中描述的对角线缩放矩阵。

特定于功能的标题

本节中的表描述了迭代显示的标题，其含义特定于您使用的优化函数。

Fgoalattain, fmincon, fminimax, and fseminf

This table describes the headings specific toFgoalattain,fmincon,fminimax，和fseminf。

Fgoalattain, fmincon, fminimax, or fseminf Heading	显示的信息
`达成因素`	达成因素的价值`Fgoalattain`
`CG-iterations`	Number of conjugate gradient iterations taken in the current iteration (see预处理共轭梯度法)
`定向衍生物`	Gradient of the objective function along the search direction
`可行性`	最大的约束违规，如果不平等约束算为`0`
`行搜索steplength`	Multiplicative factor that scales the search direction (seeEquation 29)
`最大约束`	内部构造和用户提供的所有约束之间的最大违规；当没有约束约束时可能是负面的
`客观价值`	Minimax问题的非线性编程重新印度的目标函数价值`fminimax`
`Procedure`	Hessian update procedures: `不可行start point` `Hessian未更新` `Hessian modified` `Hessian modified twice` 有关更多信息，请参阅更新Hessian矩阵。 QP子问题程序： `依赖`- 求解器检测并删除了依赖（冗余）平等约束。 `不可行`— The QP subproblem with linearized constraints is infeasible. `过度约束`— The QP subproblem with linearized constraints is infeasible. `Unbounded`- QP子问题是可行的，具有较大的负曲率。 `Ill-posed`- QP子问题搜索方向太小。 `不可靠`— The QP subproblem seems to be poorly conditioned.
`steplength`	Multiplicative factor that scales the search direction (seeEquation 29)
`信任区域半径`	Current trust-region radius

fminbnd and fzero

This table describes the headings specific tofminbnd和fzero。

fminbnd或fzero标题显示的信息

fminbnd或fzero标题	显示的信息
`Procedure`	程序`fminbnd`: `最初的` `金的`（金段搜索） `parabolic`(parabolic interpolation) 程序`fzero`: `最初的`(initial point) `search`（搜索包含零的间隔） `bisection` `在terpolation`（线性插值或逆二次插值）
`x`	当前点的算法

Procedure

程序fminbnd:

最初的
金的（金段搜索）
parabolic(parabolic interpolation)

程序fzero:

最初的(initial point)
search（搜索包含零的间隔）
bisection
在terpolation（线性插值或逆二次插值）

x

当前点的算法

fminsearch

This table describes the headings specific tofminsearch。

fminsearch标题显示的信息

fminsearch标题	显示的信息
`最小f（x）`	当前单纯形中的最小功能值
`Procedure`	当前迭代处的单纯形过程。程序包括： `初始单纯形` `扩张` `reflect` `shrink` `contract inside` `外面合同` For details, seefminsearch算法。

最小f（x）

当前单纯形中的最小功能值

Procedure

当前迭代处的单纯形过程。程序包括：

初始单纯形
扩张
reflect
shrink
contract inside
外面合同

For details, seefminsearch算法。

fminunc

This table describes the headings specific tofminunc。

fminunc标题	显示的信息
`CG-iterations`	Number of conjugate gradient iterations taken in the current iteration (see预处理共轭梯度法)
`行搜索steplength`	Multiplicative factor that scales the search direction (seeEquation 11)

Thefminunc“准牛顿”算法can issue askipped updatemessage to the right of the一阶最优性柱子。此消息意味着fminuncdid not update its Hessian estimate, because the resulting matrix would not have been positive definite. The message usually indicates that the objective function is not smooth at the current point.

FSOLVE

This table describes the headings specific toFSOLVE。

FSOLVE标题	显示的信息
`定向衍生物`	Gradient of the function along the search direction
`Lambda`	λ_k定义的值Levenberg-Marquardt方法
`Residual`	Residual (sum of squares) of the function
`信任区域半径`	Current trust-region radius (change in the norm of the trust-region radius)

在tlinprog

This table describes the headings specific to在tlinprog。

intlinprog标题	显示的信息
`nodes explored`	Cumulative number of explored nodes
`总时间`	自几秒钟以来的时间`在tlinprog`started
`num int solution`	Number of integer feasible points found
`整数FVAL`	Objective function value of the best integer feasible point found. This value is an upper bound for the final objective function value
`relative gap (%)`	$\frac{100 (b - a)}{\| b \| + 1},$ where b是最佳整数可行点的目标函数值。 a是目标函数值的最佳下限。 Note Although you specify`相对观念`as a decimal number, the iterative display and`output.RelativeGap`report the gap as a percentage, meaning 100 times the measured relative gap. If the exit message refers to the relative gap, this value is the measured relative gap, not a percentage.

linprog

This table describes the headings specific tolinprog。每种算法都有自己的迭代显示。

linprog标题	显示的信息
`Primal Infeas A*x-b`或者`Primal Infeas`	原始的不可行，量度违规的量度，在解决方案下应为零。 For definitions, seePredictor-Corrector(`“内点”`）或者主要算法(`'interior-point-legacy'`）或者Dual-Simplex Algorithm。
`双Infeas a'*y+z-w-f`或者`双重信息`	双重不可行性，是拉格朗日衍生物的量度，在溶液下应为零。对于拉格朗日的定义，请参阅Predictor-Corrector。为了definition of dual infeasibility, seePredictor-Corrector(`“内点”`）或者主要算法(`'interior-point-legacy'`）或者Dual-Simplex Algorithm。
`Upper Bounds {x}+s-ub`	Upper bound feasibility.{x}意思是那些x具有有限的上限。这个值是r_u残留内点线性编程。
`Duality Gap x'z+s'w`	Duality gap (see内点线性编程) between the primal objective and the dual objective.`s`和`w`仅当问题具有有限的上限时，才会出现在此方程中。
`总REL错误`	Total relative error, described at the end of主要算法
`互补性`	A measure of the Lagrange multipliers times distance from the bounds, which should be zero at a solution. See ther_cvariable in停止条件。
`Time`	Time in seconds that`linprog`已经运行

lsqlin

Thelsqlin“内点”iterative display is inherited from theQuadprogiterative display. The relationship between these functions is explained in线性最小二乘：内点或主动设置。For iterative display details, seeQuadprog。

lsqnonlin and lsqcurvefit

This table describes the headings specific tolsqnonlin和lsqcurvefit。

LSQNONLIN或LSQCURVEFIT标题	显示的信息
`定向衍生物`	Gradient of the function along the search direction
`Lambda`	λ_k定义的值Levenberg-Marquardt方法
`Resnorm`	Value of the squared 2-norm of the residual at`x`
`Residual`	Residual vector of the function

Quadprog

This table describes the headings specific toQuadprog。只有“内点凸”算法具有迭代显示。

Quadprog标题	显示的信息
`Primal Infeas`	原始的不可行，定义为`max( norm(Aeqx - beq, inf), abs(min(0, min(Ax-b))) )`
`双重信息`	Dual infeasibility, defined as`norm(Hx + f - Alambda_ineqlin - Aeq*lambda_eqlin, inf)`
`互补性`	衡量非活动不平等的Lagrange乘数的最大绝对值，该量度应在解决方案时为零。这个数量是g在可观的检测。