Superlinear Convergence of Symmetric Huang's Class of Methods.
Sur la convergence de la méthode d'Adomian
Sur la convergence théorique de la méthode du gradient réduit généralisé.
Sur la dérivation numérique en optimisation
Sur la méthode de sur-relaxation, dans le cas des problèmes avec contrainte : un résultat de convergence asymptotique
The adaptation of the -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm
We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse is viewed as a Mahalanobis circle with center , radius , and some positive definite matrix . A very efficient method for solving this problem is proposed. The method uses a modification of the -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers are determined...
The classic differential evolution algorithm and its convergence properties
Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the...
The computation of Stiefel-Whitney classes
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...
The Convergence of Matrices Generated by Rank-2 Methods from the Restricted ß-Class of Broyden.
The determination of direct control algorithms activation moments using a real-time scheduling algorithm
The labeling method on two-dimensional networks
The maximal solution of a restricted subadditive inequality in numerical analysis.
The method of bilinear programming for nonconvex quadratic programming
The Metric Gradient in Normed Linear Spaces.
The Nonlinear Programming Method of Wilson, Han, and Powell with an Augmented Lagrangian Type Line Search Function. Part 1 : Convergence Analysis.
The Nonlinear Programming Method of Wilson, Han, and Powell with an Augmented Lagrangian Type Line Search Function. Part 2 : An Efficient Implementation with Linear Least Squares Subproblems.
The second-order methods in discrete optimal control problems
The single (and multi) item profit maximizing capacitated lot–size (PCLSP) problem with fixed prices and no set–up
This paper proposes a specialized LP-algorithm for a sub problem arising in simple Profit maximising Lot-sizing. The setting involves a single (and multi) item production system with negligible set-up costs/times and limited production capacity. The producer faces a monopolistic market with given time-varying linear demand curves.
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...