论文标题
投影到二次超曲面
Projection onto quadratic hypersurfaces
论文作者
论文摘要
我们解决了将要点投射到二次超表面的问题，更具体地说是一个中心四边形。我们展示了该问题如何减少到标量值非线性函数的给定词。我们将投影的最佳解决方案之一完全描述为在给定间隔上该非线性函数的唯一根，或者是属于有限的可计算解决方案集的点。然后，我们利用了这一投影以及分裂方法的最新进步，将投影计算到盒子的交叉点，以及与交替的投影和道格拉斯 - rachford分裂方法的二次超曲面。我们在电力系统文献中对实用问题进行了测试，并表明它们在目标，执行时间和解决方案的可行性方面都超过了ipopt和gurobi。
We address the problem of projecting a point onto a quadratic hypersurface, more specifically a central quadric. We show how this problem reduces to finding a given root of a scalar-valued nonlinear function. We completely characterize one of the optimal solutions of the projection as either the unique root of this nonlinear function on a given interval, or as a point that belongs to a finite set of computable solutions. We then leverage this projection and the recent advancements in splitting methods to compute the projection onto the intersection of a box and a quadratic hypersurface with alternating projections and Douglas-Rachford splitting methods. We test these methods on a practical problem from the power systems literature, and show that they outperform IPOPT and Gurobi in terms of objective, execution time and feasibility of the solution.
