【摘要】 针对求解二次半定规划问题时收敛速度缓慢,且由于二次半定规划的对偶问题的最优条件与变分不等式的投影方程等价,则可将原问题转化为求解变分不等式问题.从一个新的角度提出了求解变分不等式问题的投影收缩算法,进而解决了该二次半定规划问题.该算法通过引入一个辅助方向来进行改进,利用两次投影的方法降低了对算子的要求,进而达到更好的收敛效果.并在算子单调的条件下给出了算法的收敛性分析和证明.更多还原

【Abstract】 For solving quadratic semi-definite programming problems where the convergence speed is slow, and because of the quadratic semi-definite programming dual problem of the optimal conditions is equivalent to the projection equation of variational inequalities, the original problem can be treated as solving variational inequality problems. This paper proposes a novel contraction projection algorithm for solving the variational inequality problems, and then apply it to solve the quadratic semi-definite programming problem. The algorithm introduces an auxiliary direction, and uses twice projection to solve the variational inequality problems. For analyzing the effect of our algorithm, this paper firstly prove its convergence property and by numerical experiment, the proposed algorithm can reduce the requirement of the operator, and also achieve faster convergence speed.更多还原