In this article, we consider the optimal coordination of automated vehicles at intersections under fixed crossing orders. We formulate problem using direct control and exploit structure to construct a semidistributed primal-dual interior-point algorithm solve it by parallelizing most computations. Differently from standard distributed optimization algorithms, where is split, in our approach spl...

In this talk, we extend our investigations on interior point methods for elliptic state-constrained optimal control problems in [4] and [2] to the parabolic case. The main difficulty of the numerical analysis of interior point methods for such problems is the lack of regularity of Lagrange multipliers associated with the state constraints. Therefore, it is helpful to improve the properties of t...

There are several classes of interior point algorithms that solve linear programming problems in O(Vin L) iterations, but it is not known whether this bound is tight for any interior point algorithm. Among interior point algorithms, several potential reduction algorithms combine both theoretical (O(+/E L) iterations) and practical efficiency as they allow the flexibility of line searches in the...

It is well known that a wide-neighborhood interior-point algorithm for linear programming performs much better in implementation than small-neighborhood counterparts. In this paper, we provide a unified way to enlarge the neighborhoods of predictorcorrector interior-point algorithms for linear programming. We prove that our methods not only enlarge the neighborhoods but also retain the so-far b...

In this paper, we first present a brief infeasible interior-point method with full-Newton step for solving linear complementarity problem (LCP). The main iteration consists of a feasibility step and several centrality steps. First we present a full Newton step infeasible interior-point algorithm based on the classic logarithmical barrier function. After that a specific kernel function is introd...

We show that recently developed interior point methods for quadratic programming and linear complementarity problems can be put to use in solving discrete-time optimal control problems, with general pointwise constraints on states and controls. We describe interior point algorithms for a discrete time linear-quadratic regulator problem with mixed state/control constraints, and show how it can b...

We present an interior proximal point method with Bregman distance, whose Bregman function is separable and the zone is the interior of the positive orthant, for solving the quasiconvex optimization problem under nonnegative constraints. We establish that the sequence generated by our algorithm is well defined and we prove convergence to a solution point when the sequence of parameters goes to ...

The simplex algorithm was the first algorithm proposed for linear programming, and although the algorithm is quite fast in practice, no variant of it is known to be polynomial time. The Ellipsoid algorithm is the first polynomial-time algorithm discovered for linear programming. The Ellipsoid algorithm was proposed by the Russian mathematician Shor in 1977 for general convex optimization proble...