可以写一段关于序贯单纯形法的matlab代码吗
时间: 2023-07-16 07:16:09 浏览: 109
当然可以,以下是一个简单的序贯单纯形法的 Matlab 代码:
```matlab
function [x, fval] = sequential_simplex(c, A, b)
% SEQUENTIAL_SIMPLEX Sequential simplex algorithm for linear programming
% [x, fval] = SEQUENTIAL_SIMPLEX(c, A, b) solves the linear programming
% problem:
%
% min c'x
% s.t. Ax <= b
% x >= 0
%
% using the sequential simplex algorithm. The problem is assumed to be
% feasible and bounded.
%
% Inputs:
% c - n-by-1 column vector of linear objective coefficients.
% A - m-by-n matrix of linear inequality constraints.
% b - m-by-1 column vector of linear inequality constants.
%
% Outputs:
% x - n-by-1 column vector of optimal primal variables.
% fval - scalar value of the optimal objective function.
[m, n] = size(A);
B = eye(m); % initial basis
x = zeros(n, 1); % initial primal variables
y = c(B)\A(:, B)'; % initial dual variables
while true
% check optimality conditions
if all(y >= 0) && all(A*x <= b)
fval = c'*x; % optimal objective function value
return
end
% select entering variable
[~, j] = min(c - y'*A);
% check unboundedness
if all(A(:, j) <= 0)
error('linear program is unbounded')
end
% select leaving variable
t = b - A*x;
t(A(:, j) <= 0) = inf;
[~, i] = min(t./A(:, j));
% update basis
B(i) = j;
% solve linear system for new dual variables
y = c(B)\A(:, B)';
% update primal variables
x = zeros(n, 1);
x(B) = c(B)\b;
end
```
该代码实现了一个简单的序贯单纯形法,用于求解线性规划问题。其中,输入参数为目标函数系数向量 $c$、约束矩阵 $A$ 和约束常数向量 $b$,输出参数为最优解 $x$ 和最优目标函数值 $fval$。在代码中,变量 $B$ 表示当前基,变量 $x$ 表示当前的原始变量,变量 $y$ 表示当前的对偶变量。在每次迭代中,根据当前基计算对偶变量 $y$,然后选择一个进入变量和一个离开变量来更新基和原始变量,直到满足最优性条件为止。
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