Ideal formulations for constrained convex optimization problems with indicator variables

Motivated by modern regression applications, in this paper, we study the convexification of a class convex optimization problems with indicator variables and combinatorial constraints on indicators. Unlike most previous work sparse problems, simultaneously consider nonlinear non-separable objective, variables, constraints. Specifically, give hull description epigraph composition one-dimensional function an affine under arbitrary As special cases result, derive ideal convexifications for hierarchy, multi-collinearity, sparsity Moreover, also short proof that separable objective function, perspective reformulation is independent from problem. Our computational experiments demonstrate potential proposed approach improving relaxation quality without significant overhead.