Abstract
We consider a convex optimization problem of two groups of variables x and y, where the objective function and the constraints are jointly convex and continuously differentiable. Supposing strong second order sufficient optimality condition (SOC), constant rank constraint qualification (CR) and using a decomposition approach with the variables x at the lower level, it is known that the marginal function ϕ(y) local can be represented as the maximum of a finite number of convex functions f i (y). Hereby the (locally defined) functions f i depend on the point y, and no such representation of ϕ is known in the neighborhood of points y where (CR) is violated.
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