In this paper, the closed-form parameterizations to the Pareto boundary for the two-user multiple-input single-output interference channel are studied. Firstly, for the equivalent channel model with each transmitter having only two antennas, the weighted sum-rate maximization (WSRMax) problem is reformulated with newly defined angle variables. Then, a centralized weighted leakage-plus-noise-to-signal ratio minimization (WLNSRMin) algorithm is proposed to find a locally optimal weighted sum-rate point. Each step of the algorithm is solved by evaluating closed-form expressions. A distributed algorithm is also given to avoid the exchange of the channel state information (CSI) between transmitters. Numerical results show that the centralized WLNSRMin algorithm converges to a local optimum of the WSRMax problem after a few iterations and the distributed algorithm achieves a performance very close to that of the centralized algorithm with only local CSI.