bv_cvxbook_extra_exercises

We assume that the sets are nonempty and that they do

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Unformatted text preview: can solve a feasibility problem: find ai , bi , such that aT x + bi > max (aT x + bj ) i j j =i if x ∈ Ci , i = 1, . . . , m, or, equivalently, aT x + bi ≥ 1 + max (aT x + bj ) i j j =i if x ∈ Ci , i = 1, . . . , m. Similarly as in part (a), we consider a robust version of this problem: maximize t subject to aT x + bi ≥ 1 + maxj =i (aT x + bj ) if dist(x, Ci ) ≤ t, j i i = 1, . . . , m. (27) The variables in the problem are ai ∈ Rn , bi ∈ R, i = 1, . . . , m, and t. Formulate the optimization problems (26) and (27) as SOCPs (if possible), or as quasiconvex optimization problems involving SOCP feasibility problems (otherwise). 7.5 Three-way linear classification. We are given data x(1) , . . . , x(N ) , y (1) , . . . , y (M ) , z (1) , . . . , z (P ) , three nonempty sets of vectors in Rn . We wish to find three affine functions on Rn , f i ( z ) = a T z − bi , i i = 1, 2, 3, that satisfy the following properties: f1 (x(j ) ) > max{f2 (x(j ) ), f3 (x(j ) )}, j = 1, . . . , N, f2 (y (j ) ) > max{f...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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