Hi,
SEE the attached file, please
I am solving an optimization problem with a second order conic programming. The objective function and constraints are all linear except for one conic constraint. I used GAMS to solve the model but it did not work.
Looking for help in selecting the right solver and how to right the constraint correctly. I am solving the model as qcp.
The attached pdf shows How I wrote the equation.
Here is a link of a paper contains the same constraint equation (42)
Article A centralized-based method to determine the local voltage co...
Dear Monsef,
I suggest you to see links and attached file on topic.
-robustlp.gms : Robust linear programming as an SOCP - GAMS
https://www.gams.com/latest/gamslib_ml/.../gamslib_robustlp.html
-Coding Second Order Cone Constraints in GAMS for MOSEK - GAMS ...
https://forum.gamsworld.org › ... › Archive Google Group
-Second Order Cone Programming | NEOS
https://neos-guide.org/content/second-order-cone-programming
-Mixed-integer second-order cone programming for lower hedging of ...
yoksis.bilkent.edu.tr/pdf/?doi=10.1007/s11590-011-0394-z
-Conic Programming - Cornell University
https://people.orie.cornell.edu/miketodd/iccopt.pdf
-Reach-Avoid Games Via Mixed-Integer Second-Order Cone ...
https://asl.stanford.edu/.../Lorenzetti.Chen.Landry.Pavone.CDC18....
Best regards
Dear Monsef,
I suggest you to see links and attached file on topic.
-robustlp.gms : Robust linear programming as an SOCP - GAMS
https://www.gams.com/latest/gamslib_ml/.../gamslib_robustlp.html
-Coding Second Order Cone Constraints in GAMS for MOSEK - GAMS ...
https://forum.gamsworld.org › ... › Archive Google Group
-Second Order Cone Programming | NEOS
https://neos-guide.org/content/second-order-cone-programming
-Mixed-integer second-order cone programming for lower hedging of ...
yoksis.bilkent.edu.tr/pdf/?doi=10.1007/s11590-011-0394-z
-Conic Programming - Cornell University
https://people.orie.cornell.edu/miketodd/iccopt.pdf
-Reach-Avoid Games Via Mixed-Integer Second-Order Cone ...
https://asl.stanford.edu/.../Lorenzetti.Chen.Landry.Pavone.CDC18....
Best regards
In addition to Mohamed-Mourad Lafifi 's resource (which would also be my first choice), you can check the GAMS model library, which to me is full of inspiration for all kinds of models. For your purpose, check out
https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_qp7.html
Thank you Prof. Armin Fügenschuh . I just solved the model by taking off the sqrt and squaring both sides. The model was correct but did not work with the original formula ( could not find explanation from the online resources but it works )
GAMS must look at the model and then figure out it can be converted to conic form. The converter will only recognize certain forms. In particular I think only certain quadratic constraints are allowed.
If you have sqrt in your model it will not work.
Btw this
https://forum.gamsworld.org/
is much better place to ask GAMS related questions.
For anyone further interested in this topic, you can also take the following GAMS definition into consideration when using Second Order Conic Programming:
*** Conic representation
* Mosek currently requires conic constraints to be of some form
* sqr(x1) + sqr(x2) + ... + sqr(xn) =L= sqr(y)
* That is, without coefficients on the xi and with single variable in each sqr().
* Also a variable xi cannot be part of more than one cone.
Variables
Pc(i,j) P variable for rotated cone
Qc(i,j) Q variable for rotated cone
IVdif(i,j) l-v difference variable for rotated cone
;
* SOC representable only if IVsum(i,j) is either nonnegative or nonpositive.
* Below we will assume that it is nonnegative.
Nonnegative Variable
IVsum(i,j) l+v sum variable for rotated cone;
Equations
Pcone(i,j) P conic equation
Qcone(i,j) Q conic equation
IVdifcone(i,j) I & V subtraction conic equation
IVsumcone(i,j) I & V sum conic equation
SecondCone(i,j) second order conic equation
;
Pcone(i,j)$LineSet(i,j) .. Pc(i,j) =e= 2*P(i,j);
Qcone(i,j)$LineSet(i,j) .. Qc(i,j) =e= 2*Q(i,j);
VVdifcone(i,j)$LineSet(i,j) .. IVdif(i,j) =e= I(i,j)-v(i);
VVsumcone(i,j)$LineSet(i,j) .. IVsum(i,j) =e= I(i,j)+v(i);
SecondCone(i,j)$LineSet(i,j) .. sqr(Pc(i,j)) + sqr(Qc(i,j)) + sqr(IVdif(i,j)) =l= sqr(IVsum(i,j));
Kind regards
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