bv_cvxbook_extra_exercises

Explain whether minimize df x y subject to x c with

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Unformatted text preview: ints can be written as N h i=1 1 + ((yi+1 − yi )/h)2 ≤ L, y1 = 0, yN +1 = 0. In addition to these constraints, we will also require that our curve passes through a set of prefixed specified points. Let F ⊆ {1, . . . , N + 1} be an index set. For j ∈ F , we require yj = yj , where fixed ∈ RN +1 (the entries of y fixed whose indices are not in F can be ignored). Finally, we add a y constraint on maximum curvature, −C ≤ (yi+2 − 2yi+1 + yi )/h2 ≤ C, i = 1, . . . , N − 1. Explain how to find the curve, i.e., y1 , . . . , yN +1 , that maximizes the area enclosed subject to these constraints, using convex optimization. Carry out your method on the problem instance with data given in iso_perim_data.m. Report the optimal area enclosed, and use the commented out code in the data file to plot your curve. Remark (for your amusement only). The isoperimetric problem is an ancient problem in mathematics with a history dating all the way back to the tragedy of queen Dido and the founding of Carthage. The story (which is mainly the account of the poet Virgil in his epic volume Aeneid ), goes that Dido was a princess forced to flee her home after her b...
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