Abstract: A new approach is proposed for the [lp] norm optimization problem by combining the Sequential Quadratic Programming（SQP） method and penalty function method. Since the initial value influences the convergence of SQP method, the penalty function is introduced to generate the feasible initial value and then solve the problem with SQP method. Numerical results show that the proposed algorithm has good performance on sparse signal reconstruction.

Key words: penalty function, sequential quadratic programming, [lp] norm, sparse signal

摘要： 结合罚函数法与序列二次规划（SQP）方法研究了[lp]范数优化的求解算法。分析了基于SQP方法的[lp]范数优化算法，探讨了初值选取对算法收敛性的影响；针对SQP方法受迭代初值的限制，引入罚函数优化方法对迭代初值作预估计，使其进入可行域，采用SQP方法求解计算。实验结果表明，结合罚函数与SQP方法的[lp]范数优化算法对稀疏信号有较优的重构效果。

关键词: 罚函数, 序列二次规划, [lp]范数, 稀疏信号