MIQP Problem Formulated as MIQCP?

GAMS
1

Hi all,

I got one issue reporting “System Failure”. My opt. problem has a mixed-integer quadratic objective function with linear constraints, and I defined it as an MIQCP problem. the report summary is as follows.

		    S O L V E      S U M M A R Y

     MODEL   dualspregu          OBJECTIVE  subdualregu
     TYPE    MIQCP               DIRECTION  MINIMIZE
     SOLVER  CPLEX               FROM LINE  666

**** SOLVER STATUS     13 System Failure           
**** MODEL STATUS      13 Error No Solution        
**** OBJECTIVE VALUE               NA

 RESOURCE USAGE, LIMIT         NA     100000000000000.000
 ITERATION COUNT, LIMIT        NA    2000000000
 EVALUATION ERRORS             NA             0
General nonlinearity detected in row subobjregu
*** Could not load data from file: Detected 1 general nonlinear rows in model

No solution returned

Actually I am aware that MIQCP is mixed-integer quadratically constrained programming, and my model is mixed-integer quadratic objective function with linear constraints, which should be termed as MIQP problem, according to IBM CPLEX website. But when I go through the GAMS CPLEX API documentation:
https://www.gams.com/latest/docs/S_CPLEX.html
I found one sentence:
"QP models are a special case that can be reformulated to have a quadratic objective function and only linear constraints. Those are automatically reformulated from GAMS QCP models. "
Then I am quite confused why it didn’t work. I also tried to term my problem as MIQP but it is not a solve keyword provided by GAMS.

Does anyone have idea for how to define a mixed-integer quadratic programming with linear constraints in GAMS? Thanks in advance.

Best,
Gabriel

2

Gabriel,

From the log output you sent I would conclude that the GAMS/CPLEX link has found a general non-linear constraint in your problem. Simply put, it does not think it is a QCP. The specific output I refer to is:

General nonlinearity detected in row subobjregu

-Steve

3

Hi,

Perhaps you have use x**2 to represent your quadratic part. **2 is the real power (https://www.gams.com/latest/docs/UG_Parameters.html#INDEX_power_2d__21_function) and can’t be used in QCP models. So better use power(x,2) or even simpler sqr(x).

-Michael

4

Thank you! Actually I was using abs() with the quadratic term. The nonlinear part of my objective function is:

subdualregu =e= ...
+ sigma/2 * sum(eg, (AEG(eg) - AEGhat(eg))) * sum(eg, (AEG(eg) - AEGhat(eg)))
+ ... ;

“…” means the linear parts and my AEG(eg) is binary variable while AEGhat(eg) is binary parameter. So I guess this is the reason why MIQCP didn’t work. In fact, this is a mixed-integer linear program with proximal regularized term, like:

I guess I cannot get rid of the absolute symbol since “x” here is a vector. I do not know if it is legal to do it this way.

Look forward to your advice.

Best,
Gabriel

5

Thank you! However, the row “subobjregu” is the row which I defined my objective function, which can be seen in the above post. I am sure that all of my constraints are mixed-integer linear. The only nonlinear and quadratic part appears in my objective function.

Best,
Gabriel

6

Unless your norm is something special, this should be written as sigma/2 * sum(eq, sqr(AEG(eg) - AEGhat(eg))).

-Michael