Geometry Control and Optimization

内点算法为求解具有各种复杂约束的优化问题提供了一种有效的工具。由于邻域点算法的迭代位于可行域的内部，因此可以以统一和简单的方式处理具有复杂边界的区域。该项目是由邻域点算法在机器人技术中的最新应用所驱动的（运动规划、触觉抓取）、语音合成（随机实现问题）、鲁棒镇定（具有频域约束的最优控制问题）和其他控制应用。它建议使用各种非标准的数学工具（约旦代数，黎曼流形，正则化行列式），以扩大的适用性的邻域点算法的新类的可行域，同时保持其效率（包括估计算法的复杂性）。

Interior-point algorithms provide an efficient tool for solving optimization problems with various complicated constraints. Since iterations of interior-point algorithms lie in the interior of a feasible domain, it is possible to treat domains with complicated boundaries in a unified and simple manner.The project is driven by recent applications of interior-point algorithms to robotics (motion planning, dextrous grasping ), speech synthesis (stochastic realization problem), robust stabilization (optimal control problems with frequency domain constraints) and other control applications. It is proposed to use various nonstandard mathematical tools (Jordan algebras, Riemannian manifolds, regularized determinants ) to expand the applicability of interior-point algorithms to new classes of feasible domains while keeping their efficiency (including estimates for the complexity of algorithms).