交替方向乘子法求解混合约束二次规划问题

Alternating direction method of multipliers for mixed constrained convex quadratic programming

针对混合约束中同时具有等式、不等式和简单凸集约束的二次规划问题,在消除不等式约束的基础上,通过引入新变量将问题等价转化为可分离优化模型,提出子问题具有封闭解形式的交替方向乘子法。数值实验结果表明,相对经典的方法,提出的方法在计算时间上有较明显的改进。

This paper aims at the quadratic programming problem with mixed constraints with equality constraints,inequality constraints and simple convex set constraints.By eliminating inequality constraints and introducing new variables,the above problem is equivalently transformed into a separable optimization model;and an alternating direction method of multipliers is proposed where all sub-problems have closed-form solutions.Numerical results show that the new method has much better performance over computational efficiency than those of classical methods.