0

There is a function in Matlab called "fmincon()". Currently, I need to solve a lagrange multiplier problem which can be solved by fmincon() function. However, the number of constrain is quite high and the constrains are nonlinear. The problem looks like this:

$\min _{c^{\prime}}\left\|c^{\prime}-c\right\|^{2}$

s.t. $\left\|x_{i}-c\right\|^{2} \leqslant d_{i},$ $1 \leqslant i \leqslant n$

In which the vector $c$, $x_{i}$ and the scalar $d_{i}$ are given, and I want to find $c^{\prime}$.

Now, the number of constrains $n$ may be quite large. I am wondering the computational complexity of that function regarding to the number and the complexity of constrains. Or just the time complexity of solving a lagrange multiplier problem.

Zhengyi Li
  • 25
  • 1
    There is not enough information in your question in order to present an answer, because we don't know what your nonlinear constraints look like, and what does your target function to be optimized look like. It is like asking: I have a big piece of metal with wings: how fast will it fly? ( without specifying anything else.) – uniquesolution Aug 15 '19 at 11:21
  • This is an absolutely model problem to solve with a second-order cone solver (SOCP) instead of a general nonlinear optimizer. – Michal Adamaszek Aug 15 '19 at 11:54
  • Yes, it is true. The econd order problem is one kind of problem I need to solve. But I also encounter problems with exponential function constrain. – Zhengyi Li Aug 15 '19 at 12:19
  • If your problem is still convex then it can likely be solved with one of the conic solvers. – Michal Adamaszek Aug 15 '19 at 12:36
  • Hey, thanks! But could I ask what is the conic solver? Has it been implemented? I am new to this field... – Zhengyi Li Aug 16 '19 at 03:03
  • https://en.wikipedia.org/wiki/Conic_optimization – Michal Adamaszek Aug 16 '19 at 06:04

0 Answers0