半定规划

Semidefinite programming

半定规划是指线性函数在对称矩阵的仿射组合半正定的约束下的极小问题 ,它实际上是凸优化问题 ,在最近的十几年中得到突飞猛进的发展 ,目前已成为优化方面最热门的领域 .这一研究活动之所以被激发起来 ,是由于半定规划在一些领域的新应用的发现以及新的有效算法的产生 .

Semidefinite programming is actually an optimization problem, which minimizes a linear object function subject to the constraints that an affine combination of symmetric matrices is positive semi-definite. It has developed tremendously in the recent decade, and it is currently considered to be the most topical area in optimization.The research is motivated by the discovery of new applications in several areas, combined with the development of efficient new algorithms. The paper serves as a general introduction to the theory and algorithm of semidefinite programming.