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Amit Bhaya - One of the best experts on this subject based on the ideXlab platform.

  • a control Liapunov Function approach to generalized and regularized descent methods for zero finding
    Hybrid Intelligent Systems, 2014
    Co-Authors: Fernando A Pazos, Amit Bhaya
    Abstract:

    This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding of ill-posed problems, showing that they can be profitably viewed as homotopy methods, in which the homotopy parameter is interpreted as a learning parameter. Moreover, it is shown that the choice of this learning parameter can be made in a natural manner from a control Liapunov Function approach CLF. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner. Adaptive regularization parameters for solving linear algebraic ill-posed problems were also proposed. This paper also shows that the discretizations of the ODEs to solve the zero finding problem, as well as the different adaptive choices of the regularization parameter, yield iterative methods for linear systems, which are also derived using the Liapunov optimizing control LOC method.

  • a control Liapunov Function approach to generalized and regularized descent methods
    2014
    Co-Authors: Fernando A Pazos, Amit Bhaya
    Abstract:

    This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding of ill-posed problems, showing that they can be profitably viewed as homotopy methods, in which the homotopy parameter is interpreted as a learning parameter. Moreover, it is shown that the choice of this learning parameter can be made in a natural manner from a control Liapunov Function approach (CLF). From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner. Adaptive regularization parameters for solving linear algebraic ill-posed problems were also proposed. This paper also shows that the discretizations of the ODEs to solve the zero finding problem, as well as the different adaptive choices of the regularization parameter, yield iterative methods for linear systems, which are also derived using the Liapunov optimizing control (LOC) method.

  • homotopy methods for zero finding from a learning control Liapunov Function viewpoint
    International Conference on Control Decision and Information Technologies, 2013
    Co-Authors: Amit Bhaya, Fernando A Pazos
    Abstract:

    This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding, showing that this class of homotopy methods can be designed in a natural manner from the control Liapunov Function (CLF) approach proposed earlier by the authors. Moreover, the CLF approach clarifies the interplay between the homotopy parameter, which can be interpreted as a learning parameter and the choice of descent direction, which is the control vector and guides the choice of both. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner.

  • control Liapunov Function design of neural networks that solve convex optimization and variational inequality problems
    Neurocomputing, 2009
    Co-Authors: Fernando A Pazos, Amit Bhaya
    Abstract:

    This paper presents two neural networks to find the optimal point in convex optimization problems and variational inequality problems, respectively. The domain of the Functions that define the problems is a convex set, which is determined by convex inequality constraints and affine equality constraints. The neural networks are based on gradient descent and exact penalization and the convergence analysis is based on a control Liapunov Function analysis, since the dynamical system corresponding to each neural network may be viewed as a so-called variable structure closed loop control system.

  • unified control Liapunov Function based design of neural networks that aim at global minimization of nonconvex Functions
    International Joint Conference on Neural Network, 2009
    Co-Authors: Fernando A Pazos, Amit Bhaya, E Kaszkurewicz
    Abstract:

    This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex Functions that have continuous first- and second-order derivatives and a unique global minimum. The approach is based on interpreting the Function as a controlled object, namely one that has an output (the Function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov Function (CLF) technique, well known in systems and control theory. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its competitors, such as the heavy ball with friction method or the more recent dynamic inertial Newton-like method.

Fernando A Pazos - One of the best experts on this subject based on the ideXlab platform.

  • a control Liapunov Function approach to generalized and regularized descent methods for zero finding
    Hybrid Intelligent Systems, 2014
    Co-Authors: Fernando A Pazos, Amit Bhaya
    Abstract:

    This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding of ill-posed problems, showing that they can be profitably viewed as homotopy methods, in which the homotopy parameter is interpreted as a learning parameter. Moreover, it is shown that the choice of this learning parameter can be made in a natural manner from a control Liapunov Function approach CLF. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner. Adaptive regularization parameters for solving linear algebraic ill-posed problems were also proposed. This paper also shows that the discretizations of the ODEs to solve the zero finding problem, as well as the different adaptive choices of the regularization parameter, yield iterative methods for linear systems, which are also derived using the Liapunov optimizing control LOC method.

  • a control Liapunov Function approach to generalized and regularized descent methods
    2014
    Co-Authors: Fernando A Pazos, Amit Bhaya
    Abstract:

    This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding of ill-posed problems, showing that they can be profitably viewed as homotopy methods, in which the homotopy parameter is interpreted as a learning parameter. Moreover, it is shown that the choice of this learning parameter can be made in a natural manner from a control Liapunov Function approach (CLF). From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner. Adaptive regularization parameters for solving linear algebraic ill-posed problems were also proposed. This paper also shows that the discretizations of the ODEs to solve the zero finding problem, as well as the different adaptive choices of the regularization parameter, yield iterative methods for linear systems, which are also derived using the Liapunov optimizing control (LOC) method.

  • homotopy methods for zero finding from a learning control Liapunov Function viewpoint
    International Conference on Control Decision and Information Technologies, 2013
    Co-Authors: Amit Bhaya, Fernando A Pazos
    Abstract:

    This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding, showing that this class of homotopy methods can be designed in a natural manner from the control Liapunov Function (CLF) approach proposed earlier by the authors. Moreover, the CLF approach clarifies the interplay between the homotopy parameter, which can be interpreted as a learning parameter and the choice of descent direction, which is the control vector and guides the choice of both. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner.

  • control Liapunov Function design of neural networks that solve convex optimization and variational inequality problems
    Neurocomputing, 2009
    Co-Authors: Fernando A Pazos, Amit Bhaya
    Abstract:

    This paper presents two neural networks to find the optimal point in convex optimization problems and variational inequality problems, respectively. The domain of the Functions that define the problems is a convex set, which is determined by convex inequality constraints and affine equality constraints. The neural networks are based on gradient descent and exact penalization and the convergence analysis is based on a control Liapunov Function analysis, since the dynamical system corresponding to each neural network may be viewed as a so-called variable structure closed loop control system.

  • unified control Liapunov Function based design of neural networks that aim at global minimization of nonconvex Functions
    International Joint Conference on Neural Network, 2009
    Co-Authors: Fernando A Pazos, Amit Bhaya, E Kaszkurewicz
    Abstract:

    This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex Functions that have continuous first- and second-order derivatives and a unique global minimum. The approach is based on interpreting the Function as a controlled object, namely one that has an output (the Function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov Function (CLF) technique, well known in systems and control theory. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its competitors, such as the heavy ball with friction method or the more recent dynamic inertial Newton-like method.

M Cadivel - One of the best experts on this subject based on the ideXlab platform.

E Kaszkurewicz - One of the best experts on this subject based on the ideXlab platform.

  • unified control Liapunov Function based design of neural networks that aim at global minimization of nonconvex Functions
    International Joint Conference on Neural Network, 2009
    Co-Authors: Fernando A Pazos, Amit Bhaya, E Kaszkurewicz
    Abstract:

    This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex Functions that have continuous first- and second-order derivatives and a unique global minimum. The approach is based on interpreting the Function as a controlled object, namely one that has an output (the Function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov Function (CLF) technique, well known in systems and control theory. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its competitors, such as the heavy ball with friction method or the more recent dynamic inertial Newton-like method.

  • threshold policies control for predator prey systems using a control Liapunov Function approach
    Theoretical Population Biology, 2005
    Co-Authors: Magno Enrique Mendoza Meza, Amit Bhaya, E Kaszkurewicz, Michel Iskin Da Silveira Costa
    Abstract:

    Abstract The stability of predator–prey models, in the context of exploitation of renewable resources, subject to threshold policies (TP) is studied in this paper using the idea of backstepping and control Liapunov Functions (CLF) well known in control theory, as well as the concept of virtual equilibria. TPs are defined and analysed for different types of one and two species predator–prey models. The models studied are the single species Noy-Meir herbivore-vegetation model, in a grazing management context, as well as the Rosenzweig–MacArthur two species predator–prey model, in a fishery management context. TPs are shown to be versatile and useful in managing renewable resources, being simple to design and implement, and also yielding advantages in situations of overexploitation.

A F Nindjin - One of the best experts on this subject based on the ideXlab platform.