SQP Algorithm C++ code for VS2005 IDE

简介：
序列二次规划算法（SQP方法）Given an estimated solution xk and taking a small step d, any arbitrary numerical optimization problem can generally be approximated in the following manner.f evaluated at x_k plus its gradient dotted with d, plus half the quadratic form involving the Hessian matrix at x_k multiplied by d squared. Similarly, h(xk+d) equals zero is derived from this expansion, while g(xk+d) being greater than or equal to zero highlights a key property of the function in that direction.subject to x = [x₁, x₂, …, xk]ᵀ and d = [d₁, d₂, …, dk]ᵀ formulate a linearly constrained quadratic minimization problem:Optimalization problem: $f(\mathbf{x}_k) + \nabla f(\mathbf{x}_k)^T \mathbf{d} + \frac{1}{2} (\mathbf{d})^T \nabla^2 f(\mathbf{x}_k) \mathbf{d}$. Subject to: Equality constraint: $\forall k, h(\mathbf{x}_k) + \nabla h(\mathbf{x}_k)^T \mathbf{d} = 0$; Inequality constraint: $\forall k, g(\mathbf{x}_k) + \nabla g(\mathbf{x}_k)^T \mathbf{d} \geq 0$.在SQP迭代过程中，QP的近似值必须是一个凸二次规划问题；其中矩阵Q等于函数f(x)在点xk处的二阶导数▽2f(xk)，它必须满足半正定条件（Q ≥ 0）。实际上，这个Q代表了目标函数f(x)关于变量x的Hessian矩阵。