Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Role of CFTR and ClC-5 in Modulating Vacuolar H(+)-ATPase Activity in Kidney Proximal Tubule

Background/Aims: It has been widely accepted that chloride ions moving along chloride channels act to dissipate the electrical gradient established by the electrogenic transport of H(+) ions performed by H(+)-ATPase into subcellular vesicles. Largely known in intracellular compartments, this mechanism is also important at the plasma membrane of cells from various tissues, including kidney. The present work was performed to study the modulation of plasma membrane H(+)-ATPase by chloride channels, in particular, CFTR and ClC-5 in kidney proximal tubule. Methods and Results: Using in vivo stationary microperfusion, it was observed that ATPase-mediated HCO(3)(-) reabsorption was significantly reduced in the presence of the Cl(-) channels inhibitor NPPB. This effect was confirmed in vitro by measuring the cell pH recovery rates after a NH(4)Cl pulse in immortalized rat renal proximal tubule cells, IRPTC. In these cells, even after abolishing the membrane potential with valinomycin, ATPase activity was seen to be still dependent on Cl(-). siRNA-mediated CFTR channels and ClC-5 chloride-proton exchanger knockdown significantly reduced H(+)-ATPase activity and V-ATPase B2 subunit expression. Conclusion: These results indicate a role of chloride in modulating plasma membrane H(+)-ATPase activity in proximal tubule and suggest that both CFTR and ClC-5 modulate ATPase activity. Copyright (C) 2010 S. Karger AG, Basel