This paper addresses the optimal design of mean-reverting portfolios (MRPs) for statistical arbitrage. The authors propose a general optimization model that simultaneously considers two key objectives: strong mean reversion (to generate frequent trading signals) and sufficient variance (to ensure profitable trades), subject to an explicit leverage constraint on the total investment. The problem is formulated as a nonconvex optimization with a smooth objective and a convex ℓ1-norm constraint. To solve it, a successive convex approximation (SCA) method is employed, which iteratively solves strongly convex surrogate problems. The inner convex subproblem is further tackled using an alternating direction method of multipliers (ADMM), which decomposes the problem into closed-form updates and a projection onto the ℓ1-ball. An Armijo-like backtracking line search is also introduced to accelerate convergence. Numerical experiments on S&P 500 data demonstrate that the proposed method achieves a favorable trade-off between mean reversion and variance, and outperforms existing approaches in terms of convergence speed and trading performance, yielding higher Sharpe ratios and cumulative returns.