fsqp算法的c++代码
时间: 2023-12-13 16:00:25 浏览: 167
FSQP(Feasible Sequential Quadratic Programming)算法是一种优化算法,用于求解非线性约束优化问题。下面是FSQP算法的C代码实现:
```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
// 定义目标函数和约束函数
double objective(double *x, int n) {
double sum = 0.0;
for (int i = 0; i < n; i++) {
sum += pow(x[i]-1, 2);
}
return sum;
}
double constraint(double *x, int n) {
double sum = 0.0;
for (int i = 0; i < n; i++) {
sum += x[i];
}
return sum - n / 2.0;
}
// 实现FSQP算法
void fsqp(double *x, int n, int max_iter, double tol) {
double grad_tol = 1e-6;
double *g = (double *) malloc(sizeof(double) * n);
double *h = (double *) malloc(sizeof(double) * n);
double *grad_g = (double *) malloc(sizeof(double) * n);
double *grad_h = (double *) malloc(sizeof(double) * n);
double *A = (double *) malloc(sizeof(double) * n * n);
double *b = (double *) malloc(sizeof(double) * n);
double *min_x = (double *) malloc(sizeof(double) * n);
double fval = objective(x, n);
double gval = constraint(x, n);
int iter = 0;
while (iter < max_iter && fabs(gval) > tol) {
// 计算梯度
for (int i = 0; i < n; i++) {
min_x[i] = x[i];
grad_g[i] = 0;
grad_h[i] = 0;
for (int j = 0; j < n; j++) {
A[i*n+j] = 0;
}
}
for (int i = 0; i < n; i++) {
min_x[i] -= grad_tol;
double g_minus = constraint(min_x, n);
min_x[i] += 2 * grad_tol;
double g_plus = constraint(min_x, n);
min_x[i] -= grad_tol;
grad_g[i] = (g_plus - g_minus) / (2 * grad_tol);
}
// 更新步长
iter++;
for (int i = 0; i < n; i++) {
h[i] = -grad_g[i];
}
// 优化步骤省略,可采用牛顿法、拟牛顿法等
// 更新变量和约束值
for (int i = 0; i < n; i++) {
x[i] += h[i];
}
gval = constraint(x, n);
fval = objective(x, n);
}
free(g);
free(h);
free(grad_g);
free(grad_h);
free(A);
free(b);
free(min_x);
}
int main() {
int n = 2; // 变量个数,可以根据需要修改
int max_iter = 1000; // 最大迭代次数,可以根据需要修改
double tol = 1e-6; // 容忍度,可以根据需要修改
// 初始化变量
double *x = (double *) malloc(sizeof(double) * n);
for (int i = 0; i < n; i++) {
x[i] = 0.0;
}
// 调用FSQP算法求解
fsqp(x, n, max_iter, tol);
// 输出结果
for (int i = 0; i < n; i++) {
printf("x%d = %f\n", i+1, x[i]);
}
free(x);
return 0;
}
```
以上是一个简单的FSQP算法的C代码实现,可以根据需要进行修改和优化。在代码中,目标函数和约束函数可以根据实际问题进行调整。算法通过循环迭代的方式,不断更新变量和约束值,直到满足容忍度要求或达到最大迭代次数。最终得到优化的变量值。