What is the ''relative mixer-integer-programming duality gap'' means ?

[Kris]

Dear Prof. Lofberg

Hello, I am working on a Distributionally robust algorithm for several months, which involves second order cone program. 

Recently, I noticed a paper named Distributionally robust optimization for energy and reserve toward a low-carbon electricity market.

In the Computational experience of section4, ''As the relative MIP duality gap set to be 10e-4, the average solution time is 239s, and the median is 235s. '' the author mentioned, which also confused me.

During the solution process of the Yalmip (I never set the duality), the command window show the value of ''Primal Objective'' column and ''Dual Objective'' column. I noticed that If the problem can be solved, the value of ''Primal Objective'' column and value of the ''Dual Objective'' column will get closed time by time.

Thus,  I guess the ''duality gap'' means the ''gap'' between  ''Primal Objective'' and ''Dual Objective''.

Can you explain me about the ''relative mixer-integer-programming duality gap'' ? 

Thanks for your patient, I'd appreciated for it if you could give me a hand.

Best wishes

Kris

[Johan Löfberg]

You would have to read the specific solver documentation on how it defines the various convergence metrics displayed

[Kris]

Thanks, I will check the document.