On two classes of matrices with positive diagonal solutions to the Lyapunov equation

AbstractWe characterize real indecomposable quasi-Jacobi matrices of class D, i.e., those which satisfy the Lyapunov equation PA + A′P = −Q with P diagonal and both P and Q positive definite. The subclass D2 (of class D) when also Q is diagonal is also characterized in the case of general indecomposable real matrices

Multiagent cooperation for solving global optimization problems: an extendible framework with example cooperation strategies

This paper proposes the use of multiagent cooperation for solving global optimization problems through the introduction of a new multiagent environment, MANGO. The strength of the environment lays in itsflexible structure based on communicating software agents that attempt to solve a problem cooperatively. This structure allows the execution of a wide range of global optimization algorithms described as a set of interacting operations. At one extreme, MANGO welcomes an individual non-cooperating agent, which is basically the traditional way of solving a global optimization problem. At the other extreme, autonomous agents existing in the environment cooperate as they see fit during run time. We explain the development and communication tools provided in the environment as well as examples of agent realizations and cooperation scenarios. We also show how the multiagent structure is more effective than having a single nonlinear optimization algorithm with randomly selected initial points