Now this is the sum of convex functions of linear (hence, affine) functions in $ (\theta, \theta_0)$. Since the sum of convex functions is a convex function, this problem is a convex optimization. …

So, the problem in the equivalent epigraph representation is still in a standard convex optimization problem form. Furthermore, for straightforward and meaningful analysis of a problem, also …

The general point of convex problems is that a local minimum is a global minimum. There are all sorts of relaxations and generalizations (or transformations as in posynomials), but generally …

In the case of a convex optimization problem, is there any obvious reason to expect that strong duality should (usually) hold? It often happens that the dual of the dual problem is the primal …

Are there any pitfalls with Approach 2 that I should be aware of? I have a convex optimization solver that seems to work well in my domain, but doesn't support box constraints. So, if there …

For what concerns my math knowledge, I am a PhD Student in Computer Science, so I (should) know intermediate math. Indeed, I know what convex functions are and how to solve a linear …

For any convex optimization problem with differentiable objective and constraint function, any points that satisfy the KKT conditions are primal and dual optimal and have zero duality gap. …

Is there any method that convert a non-convex problem to a convex one? Ask Question Asked 11 years, 6 months ago Modified 11 years, 6 months ago

Jan 8, 2018 · Having said all this: in practice, we define a convex optimization problem as one having only affine equality constraint functions and convex inequality constraint functions. …

I think one of the KKT points would guarantee optimality only when the strong duality holds (irrespective of the fact whether it's convex or non-convex). This has clarified in Boyd and …