Une application de la théorie du contrôle optimal en ultracentrifugation
Une méthode de réduction des variables appliquée au contrôle optimal de systèmes gouvernés par des équations différentielles
Une méthode directe de minimisation et applications
Une méthode multigrille pour la solution des problèmes d'obstacle
Uniform Convergence of the Newton Method for Aubin Continuous Maps
* 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...
Variable metric method with limited storage for large-scale unconstrained minimization
Variational approximation methods for eigenvalues. Convergence theorems
Variational inequalities in Banach spaces
Variational problems with moving boundaries using decomposition method.
Vectorization of bitmaps based on the LSQ method
Weierstrass-type maximum principle for microstructure in micromagnetics.
Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method
Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.
Weight minimization of elastic bodies weakly supporting tension. II. Domains with two curved sides
Extending the results of the previous paper [1], the authors consider elastic bodies with two design variables, i.e. "curved trapezoids" with two curved variable sides. The left side is loaded by a hydrostatic pressure. Approximations of the boundary are defined by cubic Hermite splines and piecewise linear finite elements are used for the displacements. Both existence and some convergence analysis is presented for approximate penalized optimal design problems.
Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
Задача равномерного приближения при оптимизации распределенной системы, описываемой уравнением параболического типа
Инфинитезимальный локальный оптимум функции множества
Итерационный метод штрафа для вариационных неравенств с сильно монотонными операторами.
К вопросу о выборе направлений спуска в задачах безусловной минимизации функций
О некоторых алгоритмах решения некорректных экстремальных задач
Один подход к получению численно реализуемых алгоритмов -субградиентного метода