Geometry Control and Optimization

内点算法为求解各种复杂约束条件下的优化问题提供了一种有效的工具。由于内点算法的迭代位于可行域的内部，因此可以统一而简单地处理边界复杂的域。该项目是由内点算法在机器人（运动规划，灵巧抓取），语音合成（随机实现问题），鲁棒稳定（频域约束下的最优控制问题）和其他控制应用中的最新应用驱动的。提出了使用各种非标准数学工具（Jordan代数、riemann流形、正则行列式）将内点算法的适用性扩展到新的可行域类，同时保持其效率（包括算法复杂性的估计）。

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).