Convex Optimization Without Slater Condition

[mertcan]

Hi, initially I am aware of the fact that when slater condition holds, then dual optimum equals primal optimum in convex optimization. But if slater condition does not hold then dual gap exist. When we have nonlinear nonconvex optimization we apply convexification of constraints including different methods. Actually we have to use convex optimization whereas we have nonlinear nonconvex optimization. So, Even we have some dual gap in our convex optimization how we can find the primal optimum value?

 

[fresh_42]

Maybe this link here can help you:
https://www.sciencedirect.com/science/article/pii/089812219190156X