精华内容
下载资源
问答
  • 非线性优化算法:各种非线性编程算法MATLAB实现
  • 利用粒子群算法非线性函数极值进行求解寻优的matlab程序代码
  • Matlab遗传算法工具箱在非线性优化中的应用-Matlab遗传算法工具箱在非线性优化中的应用.pdf 摘 要:投影寻踪是一种降维处理技术,通过它可以将多维分析问题通过投影方向转化为一维问题分析。应用该法的关 键在于...
  • Matlab中解形如下式的线性规划...在Matlab中提供了linprog函数进行线性优化的求解: eg: [x,fval,exitflag,output,lambda] = linprog(f,A,b,Aeq,beq,lb,ub,options) 函数的输入f, 即为优化对象f, A,b, Aeq, beq...

    在Matlab中解形如下式的线性规划问题:
    在这里插入图片描述
    其中包括优化对象 f’ * x, 不等式约束,等式约束,以及约束变量的上下界。
    在Matlab中提供了linprog函数进行线性优化的求解:
    eg:
    [x,fval,exitflag,output,lambda] = linprog(f,A,b,Aeq,beq,lb,ub,options)
    函数的输入f, 即为优化对象f, A,b, Aeq, beq, lb,ub 均为上式中的具体表达。最后的options是对优化过程进行参数设置,主要的包括:

    options = optimoptions(‘linprog’,‘Algorithm’,‘interior-point’,‘Display’,‘iter’,‘MaxIterations’,10)

    选择优化方法: 线性优化
    选择优化算法: 内点法(线性优化中还提供其他算法)
    显示: 显示循环次数
    限制循环次数

    还有其他参数可以设置:具体的搜索Matlab reference中的 Optimization Options Reference获得。
    举个例子:
    我们解下面的线性规划问题:

    f = [-2;-1;1];
    
    A = [1 4 -1; 2 -2 1];
    
    b = [4;12];
    
    Aeq = [1 1 2];
    beq = 6;
    
    lb = zeros(3,1);
    

    给出对应优化参数设置并求解:

    options = optimoptions('linprog','Algorithm','dual-simplex','Display','iter','MaxIterations',10)
    
    [x,fval,exitflag,output,lambda]  = linprog(f,A,b,Aeq,beq,lb,ub,options)
    

    我们可以获得如下的结果:

    options = 
    
      linprog options:
    
       Options used by current Algorithm ('dual-simplex'):
       (Other available algorithms: 'interior-point', 'interior-point-legacy')
    
       Set properties:
                  Algorithm: 'dual-simplex'
                    Display: 'iter'
              MaxIterations: 10
    
       Default properties:
        ConstraintTolerance: 1.0000e-04
                    MaxTime: Inf
        OptimalityTolerance: 1.0000e-07
    
    
    LP preprocessing removed 0 inequalities, 0 equalities,
    0 variables, and added 0 non-zero elements.
    
     Iter      Time            Fval  Primal Infeas    Dual Infeas  
        0     0.001    0.000000e+00   6.999174e+00   1.113300e+00  
        2     0.002   -1.080000e+01   1.750843e+00   0.000000e+00  
        4     0.002   -8.666667e+00   0.000000e+00   0.000000e+00  
    
    Optimal solution found.
    
    
    x =
    
        4.6667
             0
        0.6667
    
    
    fval =
    
       -8.6667
    
    
    exitflag =
    
         1
    
    
    output = 
    
      struct with fields:
    
             iterations: 4
        constrviolation: 8.8818e-16
                message: 'Optimal solution found.'
              algorithm: 'dual-simplex'
          firstorderopt: 7.4015e-16
    
    
    lambda = 
    
      struct with fields:
    
          lower: [3×1 double]
          upper: [3×1 double]
          eqlin: 0.3333
        ineqlin: [2×1 double]
    

    其中包括了对参数的显示,每一步循环的数据,以及最终的最优点的值和函数值。

    展开全文
  • Matlab线性/非线性规划优化算法(3)

    千次阅读 2020-01-27 17:11:48
    本文开始介绍非线性规划函数fmincon的用法,这个函数解决的典型问题是: 和上两个规划很相似,有等式约束和不等式约束,在不等式约束中还可以存在非线性约束。可以有的写法如下: >> help fmincon fmincon - ...

    本文开始介绍非线性规划函数fmincon的用法,这个函数解决的典型问题是:
    在这里插入图片描述
    和上两个规划很相似,有等式约束和不等式约束,在不等式约束中还可以存在非线性约束。可以有的写法如下:

    >> help fmincon
    fmincon - Find minimum of constrained nonlinear multivariable function
    
        Nonlinear programming solver.
    
        x = fmincon(fun,x0,A,b)
        x = fmincon(fun,x0,A,b,Aeq,beq)
        x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub)
        x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
        x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
        x = fmincon(problem)
        [x,fval] = fmincon(___)
        [x,fval,exitflag,output] = fmincon(___)
        [x,fval,exitflag,output,lambda,grad,hessian] = fmincon(___)
    
        See also fminbnd, fminsearch, fminunc, optimoptions, optimtool
    
        Documentation for fmincon
    

    有兴趣的可以每个都试一下,但我就只用最复杂的那个作为示例来展示了:
    我们现在有这个一个非线性优化函数:fun = @(x)100*(x(2)-x(1)2)2 + (1-x(1))^2;需要优化,我手动的给他添加了所有种类的约束:
    包括:1, 不等式约束Ax ≤ b : A = [1,2]; b = 1;
    2, 等式约束: Aeq
    x = beq Aeq = [2,1]; beq = 1;
    3, 自变量上下界: lb = [0,0]; ub = [1,2];
    4,非线性约束: nonlinear, 这个函数内部意思就是自变量被约束在一个圆的内部。
    5,优化参数设置: 我要求他使用内点法求解,如果不设置,matlab默认求解器应该是sqp
    最后给出代码:

    %% the use of fmincon
    clc
    clear all
    
    x0 = [0.1 0.3];
    A = [1,2];
    b = 1;
    Aeq = [2,1];
    beq = 1;
    lb = [0,0.2];
    ub = [0.5,0.8];
    nonlcon = @nonlinear;
    options = optimoptions('fmincon','Display','iter','Algorithm','interior-point');
    fun = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
    
      [x,fval,exitflag,output,lambda,grad,hessian] ...
        = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
        
    
      %% fmincon with gradient
      clc
    clear all
    
    x0 = [0.1 0.3];
    A = [1,2];
    b = 1;
    Aeq = [2,1];
    beq = 1;
    lb = [0,0.2];
    ub = [0.5,0.8];
    nonlcon = @nonlinear;
    options = optimoptions('fmincon','Display','iter','Algorithm','interior-point','SpecifyObjectiveGradient',true);
    fun = @rosenbrockwithgrad;
    
      [x,fval,exitflag,output,lambda,grad,hessian] ...
        = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
        
     %% fmincon using problem structure
    options = optimoptions('fmincon','Display','iter','Algorithm','interior-point');
    problem.options = options;
    problem.solver = 'fmincon';
    problem.objective = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
    problem.x0  = [0.1 0.3];
    problem.A =  [1,2];
    problem.b = 1;
    problem.beq = 1;
    problem.Aeq = [2,1];
    problem.lb = [0,0.2];
    problem.ub = [0.5,0.8];
    problem.nonlcon = @unitdisk;
     
      [x,fval,exitflag,output,lambda,grad,hessian] ...
     = fmincon(problem)
        
    

    这里面有三种写法,第一种就是普通写法,第二种我们刻意加入了梯度信息,第三种我们使用了problem structure写法,其中需要调用的函数,下面给出,

    function [c,ceq] = unitdisk(x)
    c = (x(1)-1/3)^2 + (x(2)-1/3)^2 - (1/3)^2;
    ceq = [ ];   
     end
    
    function [c,ceq] = nonlinear(x)
    c = (x(1)-1/3)^2 + (x(2)-1/3)^2 - (1/3)^2;
    ceq = [];
    end
    
    function [f,g] = rosenbrockwithgrad(x)
    % Calculate objective f
    f = 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;
    
    if nargout > 1 % gradient required
        g = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1));
            200*(x(2)-x(1)^2)];
    end
    
    

    按照我的要求,输出了相关中间变量和参数:

                                                        First-order      Norm of
     Iter F-count            f(x)  Feasibility   optimality         step
        0       3    9.220000e+00    5.000e-01    1.687e+01
        1       6    1.474360e+00    1.666e-01    2.284e+01    2.382e-01
        2       9    5.478845e-01    0.000e+00    1.247e+01    8.242e-02
        3      12    5.792800e-01    0.000e+00    4.196e-01    2.670e-03
        4      15    5.437391e-01    0.000e+00    2.104e-02    3.037e-03
        5      18    5.215088e-01    0.000e+00    5.309e-03    2.037e-03
        6      21    5.202050e-01    0.000e+00    2.002e-04    1.232e-04
        7      24    5.200021e-01    0.000e+00    2.017e-06    1.921e-05
    
    Local minimum found that satisfies the constraints.
    
    Optimization completed because the objective function is non-decreasing in 
    feasible directions, to within the value of the optimality tolerance,
    and constraints are satisfied to within the value of the constraint tolerance.
    
    <stopping criteria details>
    
    x =
    
        0.4000    0.2000
    
    
    fval =
    
        0.5200
    
    
    exitflag =
    
         1
    
    
    output = 
    
      struct with fields:
    
             iterations: 7
              funcCount: 24
        constrviolation: 0
               stepsize: 1.9214e-05
              algorithm: 'interior-point'
          firstorderopt: 2.0170e-06
           cgiterations: 0
                message: '↵Local minimum found that satisfies the constraints.↵↵Optimization completed because the objective function is non-decreasing in ↵feasible directions, to within the value of the optimality tolerance,↵and constraints are satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization completed: The relative first-order optimality measure, 2.521268e-07,↵is less than options.OptimalityTolerance = 1.000000e-06, and the relative maximum constraint↵violation, 0.000000e+00, is less than options.ConstraintTolerance = 1.000000e-06.↵↵'
    
    
    lambda = 
    
      struct with fields:
    
             eqlin: 3.8000
          eqnonlin: [0×1 double]
           ineqlin: 9.8723e-06
             lower: [2×1 double]
             upper: [2×1 double]
        ineqnonlin: 2.2644e-05
    
    
    grad =
    
       -7.6000
        8.0001
    
    
    hessian =
    
      136.0238 -148.9825
     -148.9825  205.5079
    

    关于如何具体描述优化问题,matlab doc里面给出了详细解释,可以去参考如果有问题,下面我摘出最重要的部分:
    fun — Function to minimize

    Initial point, specified as a real vector or real array. Solvers use the number of elements in, and size of, x0 to determine the number and size of variables that fun accepts.

    ‘interior-point’ algorithm — If the HonorBounds option is true (default), fmincon resets x0 components that are on or outside bounds lb or ub to values strictly between the bounds.

    ‘trust-region-reflective’ algorithm — fmincon resets infeasible x0 components to be feasible with respect to bounds or linear equalities.

    ‘sqp’, ‘sqp-legacy’, or ‘active-set’ algorithm — fmincon resets x0 components that are outside bounds to the values of the corresponding bounds.

    Example: x0 = [1,2,3,4]

    A — Linear inequality constraints

    Linear inequality constraints, specified as a real matrix. A is an M-by-N matrix, where M is the number of inequalities, and N is the number of variables (number of elements in x0). For large problems, pass A as a sparse matrix.

    A encodes the M linear inequalities

    A*x <= b,

    where x is the column vector of N variables x(😃, and b is a column vector with M elements.

    For example, to specify

    x1 + 2x2 ≤ 10
    3x1 + 4x2 ≤ 20
    5x1 + 6x2 ≤ 30,

    enter these constraints:

    A = [1,2;3,4;5,6];
    b = [10;20;30];

    b — Linear inequality constraints
    Linear inequality constraints, specified as a real vector. b is an M-element vector related to the A matrix. If you pass b as a row vector, solvers internally convert b to the column vector b(😃. For large problems, pass b as a sparse vector.

    b encodes the M linear inequalities

    A*x <= b,

    where x is the column vector of N variables x(😃, and A is a matrix of size M-by-N.

    For example, to specify

    x1 + 2x2 ≤ 10
    3x1 + 4x2 ≤ 20
    5x1 + 6x2 ≤ 30,

    enter these constraints:

    A = [1,2;3,4;5,6];
    b = [10;20;30];

    Aeq — Linear equality constraints
    Linear equality constraints, specified as a real matrix. Aeq is an Me-by-N matrix, where Me is the number of equalities, and N is the number of variables (number of elements in x0). For large problems, pass Aeq as a sparse matrix.

    Aeq encodes the Me linear equalities

    Aeq*x = beq,

    where x is the column vector of N variables x(😃, and beq is a column vector with Me elements.

    For example, to specify

    x1 + 2x2 + 3x3 = 10
    2x1 + 4x2 + x3 = 20,

    enter these constraints:

    Aeq = [1,2,3;2,4,1];
    beq = [10;20];

    beq — Linear equality constraints
    Linear equality constraints, specified as a real vector. beq is an Me-element vector related to the Aeq matrix. If you pass beq as a row vector, solvers internally convert beq to the column vector beq(😃. For large problems, pass beq as a sparse vector.

    beq encodes the Me linear equalities

    Aeq*x = beq,

    where x is the column vector of N variables x(😃, and Aeq is a matrix of size Me-by-N.

    For example, to specify

    x1 + 2x2 + 3x3 = 10
    2x1 + 4x2 + x3 = 20,

    enter these constraints:

    Aeq = [1,2,3;2,4,1];
    beq = [10;20];

    nonlcon — Nonlinear constraints
    Nonlinear constraints, specified as a function handle or function name. nonlcon is a function that accepts a vector or array x and returns two arrays, c(x) and ceq(x).

    c(x) is the array of nonlinear inequality constraints at x. fmincon attempts to satisfy

    c(x) <= 0 for all entries of c.

    ceq(x) is the array of nonlinear equality constraints at x. fmincon attempts to satisfy

    ceq(x) = 0 for all entries of ceq.

    For example,

    x = fmincon(@myfun,x0,A,b,Aeq,beq,lb,ub,@mycon)
    where mycon is a MATLAB function such as

    function [c,ceq] = mycon(x)
    c = … % Compute nonlinear inequalities at x.
    ceq = … % Compute nonlinear equalities at x.
    If the gradients of the constraints can also be computed and the SpecifyConstraintGradient option is true, as set by
    options = optimoptions(‘fmincon’,‘SpecifyConstraintGradient’,true)
    then nonlcon must also return, in the third and fourth output arguments, GC, the gradient of c(x), and GCeq, the gradient of ceq(x). GC and GCeq can be sparse or dense. If GC or GCeq is large, with relatively few nonzero entries, save running time and memory in the interior-point algorithm by representing them as sparse matrices. For more information, see Nonlinear Constraints.

    最后还有点值得一说,要注意输出宗量exitflag, 并不是所有解都是可行解,迭代退出的原因就是由exitflag指代的,只有flag>0的时候,迭代才算是正常完成。具体的指代如下:

    All Algorithms:

    1

    First-order optimality measure was less than options.OptimalityTolerance, and maximum constraint violation was less than options.ConstraintTolerance.

    0

    Number of iterations exceeded options.MaxIterations or number of function evaluations exceeded options.MaxFunctionEvaluations.

    -1

    Stopped by an output function or plot function.

    -2

    No feasible point was found.

    All algorithms except active-set:

    2

    Change in x was less than options.StepTolerance and maximum constraint violation was less than options.ConstraintTolerance.

    trust-region-reflective algorithm only:

    3

    Change in the objective function value was less than options.FunctionTolerance and maximum constraint violation was less than options.ConstraintTolerance.

    active-set algorithm only:

    4

    Magnitude of the search direction was less than 2*options.StepTolerance and maximum constraint violation was less than options.ConstraintTolerance.

    5

    Magnitude of directional derivative in search direction was less than 2*options.OptimalityTolerance and maximum constraint violation was less than options.ConstraintTolerance.

    interior-point, sqp-legacy, and sqp algorithms:

    -3

    Objective function at current iteration went below options.ObjectiveLimit and maximum constraint violation was less than options.ConstraintTolerance.

    展开全文
  • Algorithm之PrA:PrA之nLP非线性规划算法+Matlab 优化工具箱的GUI求解非线性规划 目录 PrA之nLP非线性规划算法 操作图文教程 PrA之nLP非线性规划算法 (1)、编写M 文件fun1.m 定义目标函数 ...

     Algorithm之PrA:PrA之nLP非线性规划算法+Matlab 优化工具箱的GUI求解非线性规划

     

     

     

    目录

    PrA之nLP非线性规划算法

    操作图文教程


     

     

     

    PrA之nLP非线性规划算法

    (1)、编写M 文件fun1.m 定义目标函数

    function f=fun1(x);
    f=sum(x.^2)+8;
    

    (2)、编写M文件fun2.m定义非线性约束条件

    function [g,h]=fun2(x);
    g=[-x(1)^2+x(2)-x(3)^2
        x(1)+x(2)^2+x(3)^3-20]; %非线性不等式约束
    h=[-x(1)-x(2)^2+2
        x(2)+2*x(3)^2-3]; %非线性等式约束

    (3)、利用已经定义好的函数fun1 和fun2。在Matlab 命令窗口运行optimtool,就打开图形界面,如图1 所示,填入有关的参数,未填入的参数取值为空或者为默认值,然后用鼠标点一下“start”按钮,就得到求解结果,再使用“file”菜单下的“Export toWorkspace…”选项,把计算结果输出到Matlab 工作空间中去。

     

    操作图文教程


     

     

     

    展开全文
  • Matlab线性/非线性规划优化算法(4)

    千次阅读 2020-01-28 13:52:54
    本文继续介绍matlab提供的其他优化求解函数,这里介绍 fminbnd, 用于查找单变量函数在定区间上的最小值, fminsearch,使用无导数法计算无约束的多变量函数的最小值 fminbnd的用法和fminunc很相似,区别就是fminunc...

    本文继续介绍matlab提供的其他优化求解函数,这里介绍

    1. fminbnd, 用于查找单变量函数在定区间上的最小值,
    2. fminsearch,使用无导数法计算无约束的多变量函数的最小值

    fminbnd的用法和fminunc很相似,区别就是fminunc功能更加强大,可以搜索多变量函数最优点,但是fminbnd只能用于单变量的无约束问题:
    典型的问题表示如下:

    在这里插入图片描述
    函数仅提供优化变量的上下界,其他约束都不允许,语法形式仅有如下几种:

    x = fminbnd(fun,x1,x2)
    x = fminbnd(fun,x1,x2,options)
    x = fminbnd(problem)
    [x,fval] = fminbnd(___)
    [x,fval,exitflag] = fminbnd(___)
    [x,fval,exitflag,output] = fminbnd(___)
    

    举个例子,我们优化函数:

    function f = scalarobjective(x)
    f = 0;
    for k = -10:10
        f = f + (k+1)^2*cos(k*x)*exp(-k^2/2);
    end
    

    主函数如下:

     %% the use of fminbnd
    options = optimset('Display','iter','PlotFcns',@optimplotfval);
    [x,fval,exitflag,output]  = fminbnd(@scalarobjective,1,3,options)
    
    

    结果如下:

     Func-count     x          f(x)         Procedure
        1        1.76393    -0.589643        initial
        2        2.23607    -0.627273        golden
        3        2.52786     -0.47707        golden
        4        2.05121    -0.680212        parabolic
        5        2.03127     -0.68196        parabolic
        6        1.99608    -0.682641        parabolic
        7        2.00586    -0.682773        parabolic
        8        2.00618    -0.682773        parabolic
        9        2.00606    -0.682773        parabolic
       10         2.0061    -0.682773        parabolic
       11        2.00603    -0.682773        parabolic
     
    Optimization terminated:
     the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 
    
    
    x =
    
        2.0061
    
    
    fval =
    
       -0.6828
    
    
    exitflag =
    
         1
    
    
    output = 
    
      struct with fields:
    
        iterations: 10
         funcCount: 11
         algorithm: 'golden section search, parabolic interpolation'
           message: 'Optimization terminated:↵ the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 ↵'
    
    

    而对于fminsearch的数学标准形式:
    在这里插入图片描述
    函数甚至不提供优化变量的上下界,仅仅能够使用无约束优化功能,提供的函数使用方式也仅有以下几种:

    x = fminsearch(fun,x0)
    x = fminsearch(fun,x0,options)
    x = fminsearch(problem)
    [x,fval] = fminsearch(___)
    [x,fval,exitflag] = fminsearch(___)
    [x,fval,exitflag,output] = fminsearch(___)
    

    举个例子,解matlab提供的rosenbrock函数:
    在这里插入图片描述

     %% the use of fminsearch\
     clc
     clear all
     
     options = optimset('Display','iter','PlotFcns',@optimplotfval,'TolCon',1e-6);
     fun = @(x)100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
    x0 = [-1.2,1];
    [x,fval,exitflag,output] = fminsearch(fun,x0,options)
    
    

    既然fminunc和fminseach都有一样的功能,我们不如做个小小的对比,fminsearch是个老一点的函数,仅仅提供Nelder-Mead simplex direct search这一种搜索方式,也就是单纯性搜索,可以看一下和fminunc提供的‘quasi-newton’或者‘trust-region’比较是什么样的:
    我们还是解同样的rosenblock函数,看迭代次数对比:

    
     %% the use of fminsearch\
     clc
     clear all
     
     options = optimset('Display','iter','PlotFcns',@optimplotfval,'TolCon',1e-6);
     fun = @(x)100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
    x0 = [-1.2,1];
    [x,fval,exitflag,output] = fminsearch(fun,x0,options)
    
    %% comparison between fminsearch and fminunc
    clc
    clear all
    
    options = optimoptions(@fminunc,'Display','iter','Algorithm','quasi-newton','PlotFcns',@optimplotfval);
    fun = @(x)100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
    x0 = [-1.2,1];
    [x,fval,exitflag,output] = fminunc(fun,x0,options)
    
    

    结果如下:

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    fminsearch result:
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Optimization terminated:
     the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 
     and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-04 
    
    
    x =
    
        1.0000    1.0000
    
    
    fval =
    
       8.1777e-10
    
    
    exitflag =
    
         1
    
    
    output = 
    
      struct with fields:
    
        iterations: 85
         funcCount: 159
         algorithm: 'Nelder-Mead simplex direct search'
           message: 'Optimization terminated:↵ the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 ↵ and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-04 ↵'
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    fminunc result:
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    x =
    
        1.0000    1.0000
    
    
    fval =
    
       2.8358e-11
    
    
    exitflag =
    
         1
    
    
    output = 
    
      struct with fields:
    
           iterations: 36
            funcCount: 138
             stepsize: 2.3879e-04
         lssteplength: 1
        firstorderopt: 1.8950e-05
            algorithm: 'quasi-newton'
              message: '↵Local minimum found.↵↵Optimization completed because the size of the gradient is less than↵the value of the optimality tolerance.↵↵<stopping criteria details>↵↵Optimization completed: The first-order optimality measure, 8.748957e-08, is less ↵than options.OptimalityTolerance = 1.000000e-06.↵↵'
    
    

    迭代次数少了很多,而且值得注意的是,这里stopping criteria fminsearch默认的是e-4, 而fminunc默认的是e-6,用的是更加严格的约束标准。
    画出来迭代曲线:

    fminunc
    在这里插入图片描述
    fminsearch
    在这里插入图片描述
    说明quasi-newton大发好啊,注意,fminunc是用不了内点法的,因为没有constraints, 我们在fmincon里面就可以用到内点法了。

    展开全文
  • matlab开发-非线性动态系统的优化算法。动态集成系统优化与参数估计(DISPE)技术
  • 值得单独一说的是fminunc, fminseach, fminbnd的区别: fminunc只能用于求解连续函数,对于变量没有限制 fminbnd只能用于求解单变量函数, fminsearch只能用于求解多变量函数, %% clc clear all ...
  • 实例: 寻找曲面到平面的最短距离: %% how the initial points affect the results clc clear all [x,y] = meshgrid(-4:0.1:4,-4:0.1:4); z = x.^2 + y.^2; mesh (x,y,z); plot3(x,y,z) ... z...
  • x0 = [1,2];
  • matlab求解非线性优化问题
  • 非线性SVM算法matlab实现

    热门讨论 2011-05-13 09:34:13
    对“data3.m”数据,用其中一半的数据采用非线性SVM算法设计分类器并画出决策面,另一半数据用于测试分类器性能。比较不同核函数的结果。(注意讨论算法中参数设置的影响。) 来自课程设计,附上matlab源代码,可以...
  • 非线性整数规划的遗传算法Matlab程序(附图)通常,非线性整数规划是一个具有指数复杂度的NP问题,如果约束较为复杂,Matlab优化工具箱和一些优化软件比如lingo等,常常无法应用,即使能应用也不能给出一个较为...
  • 想要最传统的多目标算法,是基于非线性优化的,这应该属于遗传算法吧,希望这个多目标算法非线性优化问题的Matlab程序
  • 蒙特卡洛算法优化非线性规划问题实例 求解此题需要三个函数文件 目标函数文件 function z=goal(x) z=3*(x(1)-2)^2+4*(x(2)-1)^2+x(1)*x(2)+2*(0.5*x(3)-3)^2; 约束条件函数文件 function lpc=lpconst(x) if 2*x(1...
  • 最近在做方程组的非线性优化问题,用到了fgoalattain函数,总结一下: 意义 解决多目标的非线性优化问题 函数形式 函数表示形式如下: 上式中,weight, goal, b和beq 是向量(组),A 和Aeq 是矩阵, c(x), ceq(x)和F...
  • Matlab 非线性有约束规划的粒子群算法

    千次阅读 多人点赞 2020-09-15 21:00:28
    适用于连续函数极值问题,对于非线性,多峰问题均有较强的全局搜索能力。 主要掌握两点 1.粒子的速度和位置 速度代表移动的快慢,位置代表移动的方向。 位置对应每个自变量,速度一般设置为变量范围的10%~20%。 2....
  • MATLAB实现非线性动态范围调整算法 实验原理 提出非线性动态范围调整,是因为线性动态范围调整的分段线性影射不够光滑。非线性动态范围调整,要求可以用光滑的曲线来实现。考虑到人眼对视觉信号的处理过程中,有一...
  • 为此,特地整理出来使用matlab求解非线性方程组的方法。 写在开头 这篇不打算对遗传算法的具体原理进行探讨,而主要是实际中的应用。在求解一些不是很复杂的非线性方程组的时候,我们在matlab使用的时候也往往不需要...

空空如也

空空如也

1 2 3 4 5 ... 20
收藏数 21,224
精华内容 8,489
关键字:

matlab非线性优化算法

matlab 订阅