In this paper we prove global convergence for first and second-order stationary points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of quadratic (or linear) models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apar...

In this paper we compare state-of-the-art multi-agent reinforcement learning algorithms in a wide variety of games. We consider two types of algorithms: value iteration and policy iteration. Four characteristics are studied: initial conditions, parameter settings, convergence speed, and local versus global convergence. Global convergence is still difficult to achieve in practice, despite existi...

This paper discusses the global output convergence for continuous time recurrent neural networks with continuous decreasing as well as increasing activation functions in probabilistic metric space. We establish three sufficient conditions to guarantee the global output convergence of this class of neural networks. The present result does not require symmetry in the connection weight matrix. The...

This paper presents a convergence proof of the adaptive tabu search (ATS) algorithms. The proof consists of two parts, i.e. convergence proof of all interested solutions in a finite search space, and that of searching processes of the ATS algorithms to the global minimum. With the proposed definitions and theorems, the proofs show that the ATS algorithms based on a random process have finite co...

Wang proposed a gradient-based neural network (GNN) to solve online matrix-inverses. Global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices. As compared to the previously-presented asymptotical convergence, this paper investigates more desirable properties of the gradient-based neural network; e.g., global exponential convergence for n...

In this paper we propose a framework for developing globally convergent batch training algorithms with adaptive learning rate. The proposed framework provides conditions under which global convergence is guaranteed for adaptive learning rate training algorithms. To this end, the learning rate is appropriately tuned along the given descent direction. Providing conditions regarding the search dir...

In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apar...

In this paper we investigate the global convergence property of the affine scaling method under the assumption of dual nondegeneracy. The behavior of the method near degenerate vertices is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous LP problems and Karmarkar's method. It is shown that the step-size 1/8, where the displacement vector is n...

This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newt...

In this paper, further results are proposed that concern the design and the convergence of receding horizon nonlinear observers. The key feature is the de nition of observability-radius in relation with a pre-speci ed compact set of initial con gurations. This enables a semi-global convergence result to be derived that turns to be a global convergence result when appropriate regularity assumpti...