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Projection method with residual selection for linear feasibility problems

100%
Dylewski R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
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tom 27
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nr 1
43-50
EN
We propose a new projection method for linear feasibility problems. The method is based on the so called residual selection model. We present numerical results for some test problems.
2
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Projection method with level control in convex minimization

100%
Dylewski R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
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tom 30
|
nr 1
101-120
EN
We study a projection method with level control for nonsmoooth convex minimization problems. We introduce a changeable level parameter to level control. The level estimates the minimal value of the objective function and is updated in each iteration. We analyse the convergence and estimate the efficiency of this method.
3
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Numerical behavior of the method of projection onto an acute cone with level control in convex minimization

88%
Dylewski R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2000
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tom 20
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nr 2
147-158
EN
We present the numerical behavior of a projection method for convex minimization problems which was studied by Cegielski [1]. The method is a modification of the Polyak subgradient projection method [6] and of variable target value subgradient method of Kim, Ahn and Cho [2]. In each iteration of the method an obtuse cone is constructed. The obtuse cone is generated by a linearly independent system of subgradients. The next approximation of a solution is the projection onto a translated acute cone which is dual to the constructed obtuse cone. The target value which estimates the minimal objective value is updated in each iteration. The numerical tests for some tests problems are presented in which the method of Cegielski [1] is compared with the method of Kim, Ahn and Cho [2].
4
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Selection strategies in projection methods for convex minimization problems

88%
Cegielski A., Dylewski R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
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nr 1
97-123
EN
We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical results show that the presented selection strategies ensure long steps and lead to an essential acceleration of the convergence of projection methods.
5
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Numerical simulations of the humid atmosphere above a mountain

75%
Bousquet A., Chekroun M. D., Hong Y., Temam R. M., Tribbia J.
Mathematics of Climate and Weather Forecasting
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2015
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tom 1
|
nr 1
EN
New avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives near the topography. Instead we implement a first order finite volume method for the spatial discretization using the initial coordinates x and p. A compatibility condition similar to that related to the condition of incompressibility for the Navier- Stokes equations, is introduced. In that respect, a version of the projection method is considered to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. For the spatial discretization, a modified Godunov type method that exploits the discrete finite-volume derivatives by using the so-called Taylor Series Expansion Scheme (TSES), is then designed to solve the equations. We report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated.
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