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On Henrici's transformation in optimization

100%
Rhanizar B.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 2
127-141
EN
Henrici's transformation is a generalization of Aitken's $Δ^2$-process to the vector case. It has been used for accelerating vector sequences. We use a modified version of Henrici's transformation for solving some unconstrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.
2
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Analysis of an isopetype dual algorithm for optimizing control and nonlinear optimization

80%
Tadej W., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 2
429-457
EN
First results concerning important theoretical properties of the dual ISOPE (Integrated System Optimization and Parameter Estimation) algorithm are presented. The algorithm applies to on-line set-point optimization in control structures with uncertainty in process models and disturbance estimates, as well as to difficult nonlinear constrained optimization problems. Properties of the conditioned (dualized) set of problem constraints are investigated, showing its structure and feasibility properties important for applications. Convergence conditions for a simplified version of the algorithm are derived, indicating a practically important threshold value of the right-hand side of the conditioning constraint. Results of simulations are given confirming the theoretical results and illustrating properties of the algorithms.
3
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Large-scale nonlinear programming algorithm using projection methods

80%
Białoń P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2000
|
tom 20
|
nr 2
171-194
EN
A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent on a large dimension of the problem. The method preserves its convergence properties under limitations in complicating sets by geometric cuts. Various aspects and variants of the method are analyzed theoretically and experimentally.
4
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Optimization-based approach to path planning for closed chain robot systems

80%
Szynkiewicz W., Błaszczyk J.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 4
659-670
EN
An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a “quasi-dynamic” NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used, which implements a nonlinear primal-dual interior-point method, one of the leading techniques for large-scale nonlinear optimization.
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