Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically ...

1. Abstract Incomplete convergence in numerical simulation such as computational physics simulations and/or Monte Carlo simulations can enter into the calculation of the objective function in an optimization problem, producing noise, bias, and topographical inaccuracy in the objective function. These affect accuracy and convergence rate in the optimization problem. This paper is concerned with ...

Simplified Dolphin Echolocation (SDE) optimization is an improved version of the Dolphin Echolocation optimization. The dolphin echolocation (DE) is a recently proposed metaheuristic algorithm, which was imitated dolphin’s hunting process. The global or near global optimum solution modeled as dolphin’s bait, dolphins send sound in different directions to discover the best bait among their searc...

In this paper, optimal placement of Phasor Measurement Unit (PMU) using Global Positioning System (GPS) is discussed. Ant Colony Optimization (ACO), Simulated Annealing (SA), Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) are used for this problem. Pheromone evaporation coefficient and the probability of moving from state x to state y by ant are introduced into the ACO. The modifi...

This paper studies the global output convergence of a class of recurrent neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying inputs. We establish two sufficient conditions for global output convergence of this class of neural networks. Symmetry in the connection weight matrix is not required in the pres...