正定二次规划的投影最小二乘算法

提出了正定二次规划问题的投影最小二乘算法．该算法先求目标函数无约束优化问题的解，再将此解逐次投影到有效约束的边界．迭代过程中不断更新有效约束，最终得到问题的有效约束集，进而得到问题的解．将该算法应用到FIR滤波器的约束最小二乘设计中，算法分析及约束FIR滤波器的设计例子都表明该算法的计算量远小于目前最流行的二次规划算法——有效集方法．

Projected least-squares algorithm for positive quadratic programming

A new efficient algorithm for quadratic programming (QP) problems is proposed. The algorithm is referred to as a projected least-squares (PLS) algorithm. In the algorithm, the unconstrained minimization solution of the quadratic objective is first computed, and then projected successively onto the boundaries of active constraints. The active constraints are updated iteratively during the iterative process, until the true active-set of the problem is found. Algorithm analysis and application in the constrained least-squares design of FIR filters shows that the PLS algorithm consumes far less amount of computation than the popular active-set methods.