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).
