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GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints
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Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [ 4 ] Binh et al. [ 5 ] and Binh. [ 6 ] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which ...
The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.
In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem.It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.
For a two dimensional phase retrieval problem, there is a degeneracy of solutions as () and its conjugate () have the same Fourier modulus. This leads to "image twinning" in which the phase retrieval algorithm stagnates producing an image with features of both the object and its conjugate. [3]
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Learn how to download and install or uninstall the Desktop Gold software and if your computer meets the system requirements.