<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt">Hello all,<br><br>i have a basic question on how the IPOPT Solver behaves when calculating nonconvex (MINLP) Problems using Branch and Bound.<br>I know that the IPOPT Solver finds locally optimal solutions, based on a randomly chosen starting point.<br><br>In my Case Bonmin finds Solutions (i did 4000 examples of different parameter values) that are very accurate. (99.82% using a MIP-Gap of 1%).<br><br>But there are runaway values. In one example i only found a solution that is 60% of the optimal value (I used full enumeration to determine the optimal solution).<br><br>Now i am asking myself how this could happen.<br>I suspect that due to a unluckyness BONMIN found a feasable solution very fast and accepted it, without solving alot of nodes.<br><br>Now my question:<br>Does Bonmin decrease the lower bound (if one is found when
solving different nodes) or is the lower bound fixed? <br>With fixed i mean that the first solution found by ipopt (where every integer is relaxed) is never changed.<br><br>In my opinion the following could happen:<br>BONMIN forces decision variables, then IPOPT finds solutions outside the local optimum (found in step one).<br>Then the lower bound would decrase. Is that the case?<br><br>In the case where the found solution was 60% BONMIN could have been unlucky and wasnt able to solve enough nodes to force the lower bound out of the local optimum?<br><br>I hope i could make myself understandable.<br>Thank you very much!<br><br><br><div><br></div></div></body></html>