Experimental results demonstrate desirable effectiveness and scalability of our approach (up to 131K processors) for solving large redistricting problems, which enables substantive research into the relationship between democratic ideals and phenomena such as partisan gerrymandering.
The key merits of ADMM is its ability to split or decouple multiple variables in optimization problems, which enables one to find a solution to a large-scale global optimization problem by coordinating solutions to smaller sub-problems.
We sharpen these old weapons with the help of submodular functions, and apply them to this problem, which enable us to design a more elaborated branching scheme on deciding whether a non-terminal vertex is with a terminal or not.
In this paper we provide a new approach to this problem which enables us first, to give a shorter proof and second, to remove dimensionality constraints completely.
We propose a solution to this problem which enables an AI system with a library of machine learning algorithms to select and sequence appropriate algorithms autonomously.
The simulation is tested extensively on a one-dimensional phase change problem which enables the comparison of the results with a existing analytical solution.
Thereby, the problem is reformulated as a well known classical control problem, which enables the use of existing tools to optimize robustness with respect to arbitrary exogenous disturbances.
First, since our patterns are not with the same length, VOM model is more adaptive in our problem which enables the state space reduced significantly.
It is guaranteed by the following reasons: first, our proposed energy functional is convex, which can result in the fast convergence; second, we apply the dual formulation to the optimization problem, which enables convergence faster.
Dynamic spectrum access (DSA) is proposed to solve the spectrum scarcity problem, which enables users to adjust communication parameters, such as operating frequency, transmission power, and modulation scheme, in response to the changes in the radio environment [1 3].
