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Not only is the continuous problem (CP 2) simpler to solve, but also, by using these two modifications, the problem (CP 2) will have discrete solutions in x which will turn out to be the solutions to our initial problem (DP 1), as we will show later on.
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"Today, part of the problem is the continuous degradation of the property because of inferior materials used in construction," said Mr. Medina, who is president of East River North Renewal.
Another problem is the continuous motion of all components induced by heart pulsation and respiration, which are most prominent in the lower and anterior sections of the chest.
Support vector regression (SVR) is an alternate version that is used for the continuous problem.
Since the traditional PSO mechanism is used to handle the continuous problem, in this paper, the discrete PSO is adopted to encode the particles as the binary variables.
This method of approximation has the advantage that the schemes can also be effective in the case when the continuous problem is considered under certain restrictions.
The proofs of these two propositions are detailed in Appendix B. The continuous problem (CP 2) is a convex optimization problem.
Let U be the exact solution of the continuous problem, and (U_{h}) be its approximate values on (overline{R}^{h}).
This is confirmed by a von Neumann stability analysis of a simplified case and is also shown to be reasonable in view of the continuous problem which contains stable and unstable modes.
We show that this full discretization scheme is consistent, stable and monotone, and hence the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed.
The importance of observing the L2 invariance of the continuous problem is demonstrated through numerical experiments.
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