Algorithm 31. The calculation of the minimum of a certain function of several variables
Algorithm. 44. MIMUN. Optimization of one-dimensional multimodal functions in the presence of noise
Algorithm 45. A heuristic algorithm for the traveling-salesman problem
Algorithm 49. An algorithm for solving the machine sequencing problem
Algorithm 5. Solution of the transportation problem by bridges dual labeling method
Algorithme d'approximation interne de problèmes de point de selle avec contraintes via l'optimisation
Algorithmes de type F.A.C. en optimisation convexe
Algorithms 77-78. Uniform approximation of empirical functions being either monotone or having a fixed number of extrema
Algorithms for Bound Constrained Quadratic Programming Problems.
Algorithms for Optimal Design with Application to Multiple Polynomial Regression.
Alguns teoremas sobre a equivalência do problema do caixeiro viajante múltiplo ao problema do caixeiro viajante
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
Alternating Iteration and Elliptic Variational Inequalities.
Amélioration de la stabilité numérique d'algorithmes de résolution de programmes linéaires à matrices de contraintes clairsemées
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An abstract version of the concentration compactness principle.
We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains.
An active set strategy based on the augmented lagrangian formulation for image restoration
An active set strategy based on the augmented Lagrangian formulation for image restoration
Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...
An adaptive finite element method for solving a double well problem describing crystalline microstructure
The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent...