【摘要】 <正>半定规划是线性规划的一种拓广,它之所以具有很强的生命力,不仅在于它在系统论、控制论、组合优化、特征值优化等诸多领域中有着广泛的应用,而且在于它为研究更广泛的凸优化问题的性质和算法提供了一种独特的方法,更主要的是它无论在理论上还是实际中都有行之有效的多项式时间算法。目前,研究较多的半定规划问题[1-3]是在满足约束“对称矩阵的仿射组合半正定”的条件下,使线性函数极小化,即线性半定规划问题.文[4]给出了更多还原

【Abstract】 In this paper, we discuss the relations among the quadratic semi-definite programming problem, the linear semi-definite programming and the linear-quadratic semi-definite programming problem. The duality theories are presented. After proving the equivalence of its optimality conditions and monotonous linear variational inequalities, we use the projection and contraction algorithms to solve (QSDP). We present the algorithms and its convergence analysis.更多还原