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41.
We introduce a class of algorithms for the solution of linear programs. This class is motivated by some recent methods suggested for the solution of complementarity problems. It reformulates the optimality conditions of a linear program as a nonlinear system of equations and applies a Newton-type method to this system of equations. We investigate the global and local convergence properties and present some numerical results. The algorithms introduced here are somewhat related to the class of primal–dual interior-point methods. Although, at this stage of our research, the theoretical results and the numerical performance of our method are not as good as for interior-point methods, our approach seems to have some advantages which will also be discussed in detail. 相似文献
42.
Kanzow Christian Raharja Andreas B. Schwartz Alexandra 《Journal of Optimization Theory and Applications》2021,189(3):793-813
Journal of Optimization Theory and Applications - A reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type... 相似文献
43.
Predictor-Corrector Smoothing Methods for Linear Programs with a More Flexible Update of the Smoothing Parameter 总被引:2,自引:0,他引:2
We consider a smoothing-type method for the solution of linear programs. Its main idea is to reformulate the corresponding central path conditions as a nonlinear system of equations, to which a variant of Newton's method is applied. The method is shown to be globally and locally quadratically convergent under suitable assumptions. In contrast to a number of recently proposed smoothing-type methods, the current work allows a more flexible updating of the smoothing parameter. Furthermore, compared with previous smoothing-type methods, the current implementation of the new method gives significantly better numerical results on the netlib test suite. 相似文献
44.
A theoretical model for the growth of single-wall carbon nanotubes produced by metal-catalyzed decomposition of hydrocarbons
and fullerenes is presented. The growth process is treated as a thermodynamic equilibrium between carbon in the gas phase
and carbon in the nanotube. The minimum possible nanotube diameters based on several published experimental conditions are
calculated by combining the free energy of the reaction with an equation derived from elastic theory. The model predicts the
possibility of generating nanotubes with extremely small diameters that are smaller than in the corresponding experiments.
Received: 18 July 2001 / Accepted: 19 November 2001 / Published online: 4 March 2002 相似文献
45.
A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems 总被引:3,自引:0,他引:3
Tecla De Luca Francisco Facchinei Christian Kanzow 《Computational Optimization and Applications》2000,16(2):173-205
In this paper we introduce a general line search scheme which easily allows us to define and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic assumptions that a search direction to be used in the general scheme has to enjoy in order to guarantee global convergence, local superlinear/quadratic convergence or finite convergence. We examine in detail several different semismooth algorithms and compare their theoretical features and their practical behavior on a set of large-scale problems. 相似文献
46.
Computational Optimization and Applications - 相似文献
47.
We introduce a projection-type algorithm for solving monotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of the corresponding operator. We prove that the whole sequence of iterates converges strongly to a solution of the variational inequality. The method uses only two projections onto the feasible set in each iteration in contrast to other strongly convergent algorithms which either require plenty of projections within a step size rule or have to compute projections on possibly more complicated sets. Some numerical results illustrate the behavior of our method. 相似文献
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Hannes Buchholzer Christian Kanzow Peter Knabner Serge Kräutle 《Computational Optimization and Applications》2011,50(2):193-221
The semismooth Newton method was introduced in a paper by Qi and Sun (Math. Program. 58:353–367, 1993) and the subsequent work by Qi (Math. Oper. Res. 18:227–244, 1993). This method became the basis of many solvers for certain classes of nonlinear systems of equations defined by a nonsmooth
mapping. Here we consider a particular system of equations that arises from the discretization of a reactive transport model
in the subsurface including mineral precipitation-dissolution reactions. The model is highly complicated and uses a coupling
of PDEs, ODEs, and algebraic equations, together with some complementarity conditions arising from the equilibrium conditions
of the minerals. The aim is to show that this system, though quite complicated, usually satisfies the convergence criteria
for the semismooth Newton method, and can therefore be solved by a locally quadratically convergent method. This gives a theoretical
sound approach for the solution of this kind of applications, whereas the geoscientist’s community most frequently applies
algorithms involving some kind of trial-and-error strategies. 相似文献