Hi all, I have some optimization problem, I have googled a lot but still did not get the exact algorithm or third-party open package to apply in it. Its type is like this, Objective function: f(x1, x2, ..., xn) (n >= 100, and f may be linear or non-linear)Constraint functions: x1 + x2 + ... + xn = 1, 1) b1 * x1 + b2 * x2 + ... + bn * xn = b, 2) c1 * x1 * x1 + c2 * x2 * x2 + ... + cn * xn * xn = c, 3) <- nonlinear constraint x1, x2, ..., xn >= 0 . To find the solution of x which lets objective function globally or locally the biggest.
I was thinking about to apply gradient descent or Levenberg-Marquardt algorithm to solve it, however, the two are used for none constraint.I also considered Lagrange multiplier method, but the system of gradient equations is nonlinear, which seems difficult to solve, Which algorithm would be proper to apply here, and is there any open package like breeze for it?Any comment or link will be helpful. Thanks a lot in advance! Zhiliang
