—We consider the set consisting of graphs of fixed order and weighted edges. The vertex set of graphs in will correspond to point masses and the weight for an edge between two vertices is a functional of the distance between them. We pose the problem of finding the best vertex po-sitional configuration in the presence of an additional proximity constraint,… (More)
— After a brief overview of the problem of finding the extremal (minimum or maximum) rank positive semidef-inite matrix subject to matrix inequalities, we identify a few new classes of such problems that can be efficiently solved. We then proceed to present an algorithm for solving the general class of rank minimization problems.
—We consider a mission in which UAVs with a capacity limit each visit () targets in a hostile environment in a cooperative manner (and return to where they departed from) such that the cost reflecting operating time and risk exposed is minimized. We first propose a mixed-integer linear programming (MILP) formulation which exactly solves the problem and then… (More)
For a given graph (or network) G, consider another graph G′ by adding an edge e to G. We propose a computationally efficient algorithm of finding e such that the second smallest eigenvalue (algebraic connectivity, λ<inf>2</inf>(G′)) of G′ is maximized. Theoretically, the proposed algorithm runs in O(4mnlog(d/∈)), where n… (More)
In this paper, we consider two problems which can be posed as spectral radius minimization problems. Firstly, we consider the fastest average agreement problem on multi-agent networks adopting a linear information exchange protocol. Mathematically, this problem can be cast as finding an optimal W ∈ R n×n such that x(k + 1)