title: implementing quadratic programming in matlab
body: <p>I come across an equation that I want to solve in this <a href="http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6130328&amp;tag=1" rel="nofollow noreferrer">paper</a>. (I'm not sure if it can be read by public). It is about minimizing equation 9 (see the attached file) subject to the constraint in equation 10.  </p>
  
  <p>n is a 3-dimensional vector (so n can be expressed as a Px3 array), and c is just a vector of length K (so c is just a 1xK array). I' (a PxL array) and l (a 3xL array) are both known. I need to find the set of n and c.  </p>
  
  <p>The paper stated that:</p>
  
  <p>'We used MATLAB implementation of the trust region reflective quadratic programming for optimization.'</p>
  
  <p>I don't know how this can be done. I am not sure if what it refers to is the <a href="http://uk.mathworks.com/help/optim/ug/quadprog.html" rel="nofollow noreferrer">quadprog</a> or just the direct use of fmincon. In either case, I have no idea how to write the objective equation and the constraints equation in the appropriate form for the function call. It would be great if someone can show me how to rewrite equation and use the 'trust region reflective quadratic programming for optimization', or provide other efficient ways to solve that equation.  </p>
  
  <p>thanks 
  <img src="https://i.stack.imgur.com/lAKEj.jpg" alt="enter image description here"></p>