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21.
L. Contesse-Becker 《Journal of Optimization Theory and Applications》1993,79(2):273-310
In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception.In proving the different results, we follow the classical primaldual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straight-forward proof of the main results.The author gratefully acknowledges the referees for their helpful comments and remarks. This research was supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Technológico de Chile). 相似文献
22.
The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper. 相似文献
23.
Daniel Maerten 《Annals of Global Analysis and Geometry》2007,32(4):391-414
We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact
and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary,
dimensionless geometric constants and some normalized Sobolev ratio. 相似文献
24.
Guillemette Chapuisat 《Journal of Differential Equations》2007,236(1):237-279
This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential. 相似文献
25.
In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of simpler linear differentialoperators and a nonlinear term. 相似文献
26.
The major goal of this paper is to examine the hypothesis that stock returns and return volatility are asymmetric, threshold nonlinear, functions of change in trading volume. A minor goal is to examine whether return spillover effects also display such asymmetry. Employing a double-threshold GARCH model with trading volume as a threshold variable, we find strong evidence supporting this hypothesis in five international market return series. Asymmetric causality tests lend further support to our trading volume threshold model and conclusions. Specifically, an increase in volume is positively associated, while decreasing volume is negatively associated, with the major price index in four of the five markets. The volatility of each series also displays an asymmetric reaction, four of the markets display higher volatility following increases in trading volume. Using posterior odds ratio, the proposed threshold model is strongly favored in three of the five markets, compared to a US news double threshold GARCH model and a symmetric GARCH model. We also find significant nonlinear asymmetric return spillover effects from the US market. 相似文献
27.
Nis Halland Tore Hansen Karl Anker Jrgensen 《Angewandte Chemie (International ed. in English)》2003,42(40):4837-4837
28.
In this paper, we formulate the l
p
-norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers. 相似文献
29.
Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.
30.