Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficient...

In this paper, it is shown that by exploiting the explicit parametric state feedback solution, it is feasible to obtain the ultimate solution to minimum sensitivity problem. A numerical algorithm for construction of a robust state feedback in eigenvalue assignment problem for a controllable linear system is presented. By using a generalized parametric vector companion form, the problem of eigen...

In this paper, we address the problem of adaptive eigenvalue decomposition (EVD). We propose a new approach, based on the optimization of the log-likelihood criterion. The parameters of the log-likelihood to be estimated are the eigenvectors and the eigenvalues of the data covariance matrix. They are actualized by means of a stochastic algorithm that requires little computational cost. Furtherm...

Applying multi-objective particle swarm optimization (MOPSO) algorithm to multi-objective design of multimachine power system stabilizers (PSSs) is presented in this paper. The proposed approach is based on MOPSO algorithm to search for optimal parameter settings of PSS for a wide range of operating conditions. Moreover, a fuzzy set theory is developed to extract the best compromise solution. T...

in this paper, a novel compensator based on magnetically controlled reactor with fixed capacitor banks (fc-mcr) is introduced and then power system stability in presence of this compensator is studied using an intelligent control method. the problem of robust fc-mcr-based damping controller design is formulated as a multi-objective optimization problem. the multi-objective problem is concocted ...

In this paper, we study the robust Rayleigh quotient optimization problems that arise when optimizing in worst-case the Rayleigh quotient of data matrices subject to uncertainties. We propose to solve such problem by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity. With this approach, we can show that a commonly used iterative method can be diverg...

We introduce a new method for the calculation of bounds on the eigenvalues of Hessian matrices of twice continuously differentiable functions. Eigenvalue bounds of Hessian matrices arise in a number of notoriously difficult tasks in computational chemical engineering. For example, Hessian matrix eigenvalue bounds are used in global nonlinear optimization, global convexity/concavity analysis in ...

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenv...

The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and p...