Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multilevel a posteriori error analysis for reaction–convection–diffusion problems

We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.     

Matrix extensions and eigenvalue completions, the generic case

In this paper we provide new necessary and sufficient conditions for the so-called eigenvalue completion problem.

     

Global Smooth Solutions of the Equations of a Viscous,Heat - Conducting,One - Dimensional Gas with Density - Dependent Viscosity

We consider initial boundary value problems for the equations of the one-dimensional motion of a viscous, heat-conducting gas with density-dependent viscosity that decreases (to zero) with decreasing density. We prove that if the viscosity does not decrease to zero too rapidly, then smooth solutions exist globally in time.     

超线性奇异边值问题解的全局结构

本文讨论一类具有奇异性的超线性边值问题.我们证明,解集存在无界连通分支.作为推论,我们在一定程度上改进了文[1]的主要结果,去掉了其主要条件.     

Vacations in GI X/M Y/1 systems and Riemann boundary value problems

We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities of the embedded Markov chain are found in terms of Riemann boundary value problems, a necessary and sufficient condition of ergodicity is proved. Explicit formulas are obtained for the case where the generating function of the arrival group size is rational. Resonance between the vacation rate and the system is studied. Complete formulas are given for the cases of single and geometric arrivals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

弹性力学的Lagrange形式：用Routh方法建立弹性有限变形问题的基本方程

将弹性有限变形问题纳入Lagrange力学的理论体系中，并用经典力学中业已存在的Routh方法构建了有限变形平面应变问题和有限变形平面应力问题的基本微分方程，讨论了有限变形大挠度问题vonkarman方程中存在的矛盾进而提出了两种改进方案．