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We discuss a numerical formulation for the cell problem related to a homogenization approach for the study of wetting on micro rough surfaces. Regularity properties of the solution are described in details and it is shown that the problem is a convex one. Stability of the solution with respect to small changes of the cell bottom surface allows for an estimate of the numerical error, at least in two dimensions. Several benchmark experiments are presented and the reliability of the numerical solution...
Atmospheric flow equations govern the time evolution of chemical concentrations in the
atmosphere. When considering gas and particle phases, the underlying partial differential
equations involve advection and diffusion operators, coagulation effects, and evaporation
and condensation phenomena between the aerosol particles and the gas phase. Operator
splitting techniques are generally used in global air quality models. When considering
organic aerosol...
The paper deals with approximations and the numerical realization of a class of hemivariational inequalities used for modeling of delamination and nonmonotone friction problems. Assumptions guaranteeing convergence of discrete models are verified and numerical results of several model examples computed by a nonsmooth variant of Newton method are presented.
The least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding...
This paper presents the solution of a basic problem defined by J. Černý which solves a concrete everyday problem in railway and road transport (the problem of optimization of time-tables by some criteria).
Optimal control problems for the heat equation with pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and...
Optimal control problems for the heat equation with pointwise
bilateral control-state constraints are considered. A locally
superlinearly convergent numerical solution algorithm is proposed
and its mesh independence is established. Further, for the
efficient numerical solution reduced space and Schur complement
based preconditioners are proposed which take into account the
active and inactive set structure of the problem. The paper ends
by numerical tests illustrating our theoretical findings and
comparing...
In this article, a technique called Meta-Optimization is used to enhance the effectiveness of bio-inspired algorithms that solve antenna array synthesis problems. This technique consists on a second optimization layer that finds the best behavioral parameters for a given algorithm, which allows to achieve better results. Bio-inspired computational methods are useful to solve complex multidimensional problems such as the design of antenna arrays. However, their performance depends heavily on the...
En este artículo estudiamos la utilización de métodos duales en el diseño de algoritmos híbridos para la resolución de problemas de "Set Partitioning" (SP). Las técnicas duales resultan de gran interés para resolver problemas con estructura combinatoria no sólo porque generan cotas inferiores sino porque, además, su utilización junto con heurísticas y procedimientos de generación de desigualdades en el diseño de algoritmos híbridos permite evaluar la calidad de las cotas superiores obtenidas. Los...
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and...
In this work, the least pointwise upper and/or lower bounds on the state variable
on a specified subdomain of a control system under piecewise constant control action are sought.
This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida
regularization of the state constraints, the problem can be solved
using a superlinearly convergent semi-smooth Newton method.
Optimality conditions are derived, convergence of the Moreau-Yosida
regularization is proved, and...
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