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The self-regular formulations lead to very accurate results.
Peng-Roos-Terlaky [2 4] proposed new variants of interior point methods (IPMs) based on self-regular barrier functions and achieved so far the best known complexity for large-update methods with a specific self-regular barrier function.
Bai et al. [6] presented a large class of eligible kernel functions, which is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non-self-regular functions as special cases.
The object-oriented design used to implement a self-regular formulation of the boundary element method is presented.
The self-regular formulation is implemented to four integral equations: the displacement boundary integral equation, and the Somigliana's integral identities for displacement, stress and strain.
Using self-regular proximity functions instead of a classical logarithmic barrier function, Peng et al. [3 5] improved the complexity of large-update IPMs for the LO problem, the SDO problem, and the SOCO problem.
Choi and Lee [18] gave primal-dual interior point algorithms by using a very simple self-regular function ψ ( t ) = 1 2 ( t − 1 t ) 2, t > 0 for the SOP and gave partial answers for the question of Baes.
Baes raised an open question in his monograph [17] as follows: The theory of self-regular functions has been created for linear programming by Jiming Peng, Cornelius Roos, and Tamás Terlaky [5].
Bai and Wang [8] obtained the best known complexity result for the SOCO problem based on a parametric kernel function including the classical logarithmic function, the prototype regular kernel function, and the non-self-regular kernel function.
Comparisons of displacements, stress and strain obtained from analytical solutions and the numerical results for bidimensional and tridimensional elastostatics problems are presented, and the self-regular formulation shows strong stability.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com