uncertain

uncertain表示这些变量是不确定的，或者作用于一系列约束，该符号可以表示对变量进行服从随机分布的采样

syntax

F=uncertain(w) % w variable
F=uncertain(W) % W constraint
F=uncertain(w, distribution)

Examples

robust optimization的建模代码如下

sdpvar x w
F = [x+w<=1];
W = [-0.5<=w<=0.5, uncertain(w)];
obj = -x;
optimize([F, W], obj);

或者等价的

sdpvar x w
F = [x+w<=1];
W = [uncertain(-0.5<=w<=0.5)];
obj=-x;
optimize([F, W], obj);

To specify random uncertainties for use in optimizers and sample. you specify the distribution, and all distribution parameters following the syntax in the RANDOM command in Statistic Toolbox

其中sample函数说明为：Draw a sample in an optimizer object and instantiates parameter
Q=sample(P, N) generates concatenated instantiated optimizer objects where samples have been drawn for all parameters with associated samples.
输入：
P：optimizer对象
N：采样的数量
输出：
Q：optimizer对象
关于optimizer对象的定义如下

OPT=optimizer(Constraints, Objective, options, x, u) exports an object that contains precompiled numerical data to be solved for varying arguments x, returning the optimal value of the expression u.ExampleThe following problem creates an LP with varying upper and lowerbounds on the decision variable.A = randn(10,3);b = rand(10,1)*19;c = randn(3,1);z = sdpvar(3,1);sdpvar UB LBConstraints = [A*z <= b, LB <= z <= UB];Objective = c'*z% We want the optimal z as a function of [LB;UB]optZ = optimizer(Constraints,Objective,[],[LB; UB],z);% Compute the optimal z when LB=1, UB = 3;zopt = optZ([1; 3])% Compute two solutions, one for (LB,UB) [1;3] and one for (LB,UB) [2;6]zopt = optZ([[1; 3], [2;6]])% A second output argument can be used to catch infeasibility[zopt,infeasible] = optZ([1; 3])% To avoid the need to vectorize in order to handle multipleparameters, a cell-based definition can be used optZ = optimizer(Constraints,Objective,[],{LB,UB},{z,sum(z)})[zopt,infeasible] = optZ({1,3});zopt{1}zopt{2}

建模代码如下

sdpvar x(2, 1) w(2, 1);
F = [-10<=x+w<=10, uncertain(w, 'normal', 1, 4)]; % constraints
P = optimizer(F, sum(x), [], w, x); % 目标为sum(x), LB, UB为空, 优化变量为w, x
Q = sample(P, 10);
plot(Q); % 绘制采样结果
xopt = Q([]);

也可以使用使用如下语法设置

F=[x+w<=1, uncertain(w, @mysampler, arg1, ...)];
F=[x+w<=1, uncertain(w, @random, 0, 1)];

Reference

YALMIP uncertain

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【OR】YALMIP uncertain

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Examples

Reference

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