1- I have an Integer Linear programming problem I solved it using CPLEX solver (mip) with optcr=0 does this provide a local optimal solution or global solution?
If a use BARON (mip) instead will it be able to provide the global optimal solution as it is a deterministic global solver? DO I have to adjust a certain parameter to get the global optimal?
2- I have a problem with quadratic objective function and linear constraints (all decision variables are continuous). So it is a convex problem. I used BARON solver to solve it. Is the solution provided the global optimal solution or do I have to adjust a certain parameter?
Thanks in advance
1- I have an Integer Linear programming problem I solved it using CPLEX solver (mip) with optcr=0 does this provide a local optimal solution or global solution?
A global optimal solution.
If a use BARON (mip) instead will it be able to provide the global optimal solution as it is a deterministic global solver? DO I have to adjust a certain parameter to get the global optimal?
BARON will also find a global optimal solution if you set optcr=0
2- I have a problem with quadratic objective function and linear constraints (all decision variables are continuous). So it is a convex problem. I used BARON solver to solve it. Is the solution provided the global optimal solution or do I have to adjust a certain parameter?
Having a quadratic objective and linear constraints does not necessarily result in a convex problem. Whether it is convex or non-convex. With optcr=0, BARON will find a global optimal solution.
If the problem is convex, you could also solve it with CPLEX (again, with optcr=0 CPLEX will find a global optimal solution)
The cplex and Baron solver manuals may be of interest to you:
https://www.gams.com/latest/docs/S_CPLEX.html
https://www.gams.com/latest/docs/S_BARON.html
I hope this helps!
“best possible” refers to the value of the best bound on the objective function value.
I hope this helps!
The “best bound” column in the CPLEX log refers to the best bound that is known so far. Look for example at the following excerpt of a CPLEX log for a maximization problem.
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
0 0 29.5688 108 29.5688 157
[...]
* 0+ 0 8.0000 26.3005 228.76%
Found incumbent of value 8.000000 after 0.17 sec. (210.88 ticks)
Detecting symmetries...
0 1 26.3005 145 8.0000 26.0000 1780 225.00%
Elapsed time = 0.17 sec. (211.37 ticks, tree = 0.01 MB, solutions = 1)
* 180+ 137 15.0000 26.0000 73.33%
Cuts: 7
Found incumbent of value 15.000000 after 0.33 sec. (450.84 ticks)
180 139 25.0000 86 15.0000 26.0000 9648 73.33%
380 298 18.2545 47 15.0000 26.0000 16231 73.33%
Cuts: 11
* 440+ 347 16.0000 25.9814 62.38%
Impl Bds: 3
Found incumbent of value 16.000000 after 0.53 sec. (770.33 ticks)
* 510+ 396 17.0000 25.9437 52.61%
Found incumbent of value 17.000000 after 0.58 sec. (832.62 ticks)
* 517 339 integral 0 18.0000 25.9437 19881 44.13%
Found incumbent of value 18.000000 after 0.58 sec. (835.88 ticks)
620 428 23.0525 69 18.0000 25.6677 22019 42.60%
Cplex starts with a bound of 29.5688. Now the bound decreases (26.3005, 26.0000, 25.9814 ,…) and the objective value of the best integer solution increases (8.0000, 15.0000, 16.0000) .
This is how the branch and bound algorithm works see e.g. (https://en.wikipedia.org/wiki/Branch_and_bound).
The CPLEX documentation on how to interpret the node log may also be of interest.
https://www.ibm.com/support/knowledgecenter/SSSA5P_12.10.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/discr_optim/mip/para/52_node_log.html
I hope this helps!
