One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectral radius—in [0,1)— of a certain matrix in the definition of the preconditioner. Spectral radius c...

Inspired by the work of Marcellini and Papi [MP] we consider local minima u: R n ⊃ Ω → RM of variational integrals of the form ∫ Ω h(|∇u|) dx and prove interior gradient bounds under rather general assumptions on h working with the additional hypothesis that u is locally bounded. Our requirements imposed on the density h do not involve the dimension n.

A practical algorithm for box-constrained optimization is introduced. The algorithm combines an active-set strategy with spectral projected gradient iterations. In the interior of each face a strategy that deals efficiently with negative curvature is employed. Global convergence results are given. Numerical results are presented.

A surface reconstruction technique based on the Lminimization of the variation of the gradient is introduced. This leads to a non-smooth convex programming problem. Well-posedness and convergence of the method is established and an interior point based algorithm is introduced. The L-surface reconstruction algorithm is illustrated on various test cases including natural and urban terrain data.

A surface reconstruction technique based on minimization of the total variation of the gradient is introduced. Convergence of the method is established, and an interior-point algorithm solving the associated linear programming problem is introduced. The reconstruction algorithm is illustrated on various test cases including natural and urban terrain data, and enhancement of low-resolution or al...

Results from 3D global gyrokinetic particle simulations of ion temperature gradient driven microturbulence in a toroidal plasma show that the ion thermal transport level in the interior region exhibits significant dependence on the ion-ion collision frequency even in regimes where the instabilities are collisionless. This is identified as arising from the Coulomb collisional damping of turbulen...

A simple procedure for coating the interior surface of Beckman Ultra-Clear centrifuge tubes with polyvinyl alcohol is described. The coated tubes are wettable and allow salt solutions to gravity-feed down their sides. This modification of the tubes permits the performance of previously developed density gradient and uniform density ultracentrifugation procedures for lipoprotein fractionation.

Let (M,g) be an n-dimensional complete Riemannian manifold with Ric(M) ≥ −(n− 1)Q, where Q ≥ 0 is a constant. We obtain an interior gradient bound for minimal graphs inM×R under some technical assumptions. For details, see Theorem 2.

We consider anisotropic variational integrals of (p, q)-growth and prove for the scalar case interior C-regularity of bounded local minimizers under the assumption that q ≤ 2p by the way discussing a famous counterexample of Giaquinta. In the vector case we obtain some higher integrability result for the gradient.