Nonmonotone globalization techniques for the Barzilai-Borwein gradient method.

In this paper we propose new globalization strategies for the Barzilai and Borwein gradient method, based on suitable relaxations of the monotonicity requirements. In particular, we define a class of algorithms that combine nonmonotone watchdog techniques with nonmonotone linesearch rules and we prove the global convergence of these schemes. Then we perform an extensive computational study, which shows the effectiveness of the proposed approach in the solution of large dimensional unconstrained optimization problems

Nonmonotone globalization of the finite-difference Newton-GMRES method for nonlinear equations.

In this paper, we study nonmonotone globalization strategies, in connection with the finite-difference inexact Newton-GMRES method for nonlinear equations. We first define a globalization algorithm that combines nonmonotone watchdog rules and nonmonotone derivative-free linesearches related to a merit function, and prove its global convergence under the assumption that the Jacobian is nonsingular and that the iterations of the GMRES subspace method can be completed at each step. Then we introduce a hybrid stabilization scheme employing occasional line searches along positive bases, and establish global convergence towards a solution of the system, under the less demanding condition that the Jacobian is nonsingular at stationary points of the merit function. Through a set of numerical examples, we show that the proposed techniques may constitute useful options to be added in solvers for nonlinear systems of equations. © 2010 Taylor & Francis

Globally convergent block-coordinate techniques for unconstrained optimization.

In this paper we define new classes of globally convergent block-coordinate techniques for the unconstrained minimization of a continuously differentiable function. More specifically, we first describe conceptual models of decomposition algorithms based on the interconnection of elementary operations performed on the block components of the variable vector. Then we characterize the elementary operations defined through a suitable line search or the global minimization in a component subspace. Using these models, we establish new results on the convergence of the nonlinear Gauss–Seidel method and we prove that this method with a two-block decomposition is globally convergent towards stationary points, even in the absence of convexity or uniqueness assumptions. In the general case of nonconvex objective function and arbitrary decomposition we define new globally convergent line-search-based schemes that may also include partial global inimizations with respect to some component. Computational aspects are discussed and, in particular, an application to a learning problem in a Radial Basis Function neural network is illustrated

On the convergence of the block nonlinear Gauss-Seidel method under convex constraints.

We give new convergence results for the block Gauss–Seidel method for problems where the feasible set is the Cartesian product of m closed convex sets, under the assumption that the sequence generated by the method has limit points. We show that the method is globally convergent for m=2 and that for m>2 convergence can be established both when the objective function f is componentwise strictly quasiconvex with respect to m−2 components and when f is pseudoconvex. Finally, we consider a proximal point modification of the method and we state convergence results without any convexity assumption on the objective functio

Convergent decomposition techniques for training RBF neural networks.

In this article we define globally convergent decomposition algorithms for supervised training of generalized radial basis function neural networks. First, we consider training algorithms based on the two-block decomposition of the network parameters into the vector of weights and the vector of centers. Then we define a decomposition algorithm in which the selection of the center locations is split into sequential minimizations with respect to each center, and we give a suitable criterion for choosing the centers that must be updated at each step. We prove the global convergence of the proposed algorithms and report the computational results obtained for a set of test problems

Physicochemical Characteristics and Macroinvertebrate Assemblages of Riffles Upstream and Downstream of a Streambank Impacted by Unrestricted Cattle Access

Riparian zones are important contributors to stream ecosystem health. Alteration of such areas can change stream structure and function, resulting in modified productivity and hydrologic patterns. We studied two riffle sites on the South Fork of the Spring River in Fulton County, AR upstream and downstream of a streambank ostensibly degraded by unrestricted cattle access. The two sites were measured for differences in physical habitat (including bank width, stream velocity, depth, substrate composition, and embeddedness), chemical characteristics (including dissolved oxygen, pH, conductivity, turbidity and total suspended solids) and biological characteristics (including benthic macroinvertebrate community composition, similarity, and standing crop). Measurements were conducted quarterly for one year. We found embeddedness, total suspended solids and turbidity to be significantly higher downstream of the cattle access area. Community metrics were similar for both sites; however, macroinvertebrate standing crop was lower downstream. These results suggest moderate differences in stream productivity downstream of the cattle access site. Future work will evaluate whether reduced cattle access and streambank stabilization efforts result in improvements in water quality and density of macroinvertebrates

Analysis of Phytoestrogens by High Performance Liquid Chromatography

Phytoestrogens are biochemicals synthesized in plants which mimic steroidal estrogen activity in mammals. Analysis of these compounds in the legumes which produce them and in body fluids is important to the study of their physiological effects. High pressure liquid chromatography (HPLC) has been found to be an efficient and sensitive method of identification and quantitation of isoflavonoids, one class of phytoestrogen. Here we report the separation of three isoflavonoids, biochanin A, genistein and daidzein using an HPLC system with a Cg reverse phase column and a linear gradient mobile phase containing acetonitrile and acetic acid/water (10/90, v/v) over 60 minutes. Minimum detection limits for the three isoflavonoids were 0.556 mug/mL, 0.314 mug/mL, and 0.377 mug/mL, respectively. This method was used to measure the concentrations of isoflavonoids in two types of soy meal and in several animal feeds. Projected use of this assay includes studies of reproductive ability following ingestion of these isoflavonoids in domestic ruminants and in wild rodents

A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations

Abstract In this paper we study a class of derivative-free unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some well-known derivativefree methods and we propose a new algorithm combining coordinate rotations with approximate simplex gradients. Through extensive numerical experimentation, we show that the proposed algorithm is highly competitive in comparison with some of the most efficient direct search methods and model based methods on a large set of test problems