  This paper tackles forecast combination with many forecasts or minimum
variance portfolio selection with many assets. A novel convex problem called
L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation
minimizes the squared Euclidean norm of the weight vector subject to a set of
relaxed linear inequality constraints. The magnitude of relaxation, controlled
by a tuning parameter, balances the bias and variance. When the
variance-covariance (VC) matrix of the individual forecast errors or financial
assets exhibits latent group structures -- a block equicorrelation matrix plus
a VC for idiosyncratic noises, the solution to L2-relaxation delivers roughly
equal within-group weights. Optimality of the new method is established under
the asymptotic framework when the number of the cross-sectional units $N$
potentially grows much faster than the time dimension $T$. Excellent finite
sample performance of our method is demonstrated in Monte Carlo simulations.
Its wide applicability is highlighted in three real data examples concerning
empirical applications of microeconomics, macroeconomics, and finance.
