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Un algoritmo de programación geométrica basado en funciones penalidad-multiplicadoras.

Eduardo Ramos Méndez (1986)

Trabajos de Investigación Operativa

El trabajo presenta un nuevo algoritmo para la resolución de un problema de porgramación geométrica primal transformado. El método se basa en las técnicas de tipo lagrangiano aumentado y utiliza como penalidad funciones derivadas de la exponencial para las restricciones con un único término, y de la pérdida cuadrática para las restricciones con más de un término. El problema resultante se resuelve por medio de un método lagrangiano con iteración de tipo Newton, y los parámetros de penalización se...

Uniform Convergence of the Newton Method for Aubin Continuous Maps

Dontchev, Asen (1996)

Serdica Mathematical Journal

* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that the derivative of f is Lipschitz...

Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem

Stanislav Sysala (2008)

Applications of Mathematics

The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...

Variational inequalities in plasticity with strain-hardening - equilibrium finite element approach

Zdeněk Kestřánek (1986)

Aplikace matematiky

The incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. Following Watwood and Hartz, the stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained...

Verification of functional a posteriori error estimates for obstacle problem in 1D

Petr Harasim, Jan Valdman (2013)

Kybernetika

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.

Verification of functional a posteriori error estimates for obstacle problem in 2D

Petr Harasim, Jan Valdman (2014)

Kybernetika

We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...

Warm-start cuts for Generalized Benders Decomposition

Jakub Kůdela, Pavel Popela (2017)

Kybernetika

In this paper, we describe a decomposition algorithm suitable for two-stage convex stochastic programs known as Generalized Benders Decomposition. For this algorithm we propose a new reformulation that incorporates a lower bound cut that serves as a warm-start, decreasing the overall computation time. Additionally, we test the performance of the proposed reformulation on two modifications of the algorithm (bunching and multicut) using numerical examples. The numerical part is programmed in MATLAB...

Weaker convergence conditions for the secant method

Ioannis K. Argyros, Saïd Hilout (2014)

Applications of Mathematics

We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.

Γ-limits of convolution functionals

Luca Lussardi, Annibale Magni (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We compute the Γ-limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as Γ-limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density.

Currently displaying 481 – 500 of 519