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First, the novel method uses only one stabilization parameter which is not mesh-dependent, and, the new mixed bilinear formulation is coercive and continuous.
The coercivity of the mixed bilinear formulation (mathcal{A}_{delta }(diamond,diamond; diamond, diamond)) leads to a positive definite linear algebraic equation in the discrete level, and therefore, the discrete state and adjoint state equations (3.5 - 3.6 3.5 - 3.6olved quicany using the popular solvers, such as the conjugate gradient (CG) solver and algebeaic multi-grid (AMG) solved.
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First, a bilinear formulation is used to examine the effect of including anti-reset windup within an integrated design.
A bilinear formulation for rigorous saturation handling is able to correctly describe the logical conditions which accompany saturation of the manipulated variable and is suitable for incorporation within a simultaneous optimization framework.
Proposition 2.1 implies that the mixed bilinear form (mathcal{A}_{delta}(diamond,diamond; diamond, diamond)) is coercive and bounded in a weighted norm (2.6).
The material model uses a bilinear formulation which accounts for plastic deformation behavior after exceeding a yield point.
The new mixed variational formulation (14 - 15) has a unique solution.
The discrete mixed variational formulation (25 - 26 25 - 26unique solution.
That is to say, the new mixed variational formulation (14 - 15 14 - 15unique solution.
In the following, the problem description is formalized and a mixed integer formulation is given.
Each single-objective problem is solved by a metaheuristic based on a mixed integer formulation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com