bv_cvxbook_extra_exercises

# You can terminate your barrier method when the

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Unformatted text preview: Solve the ML estimation problem with data deﬁned in one_bit_meas_data.m, using Newton’s method with backtracking line search. This ﬁle will deﬁne a matrix A (with rows aT ), a vector i b, and a vector y with elements ±1. ¯ Remark. The Matlab functions erfc and erfcx are useful to evaluate the following functions: 1 √ 2π 1 2 √ eu /2 2π u −∞ u −∞ e− t e− t 2 /2 2 /2 1 √ 2π 1 u dt = erfc(− √ ), 2 2 u 1 dt = erfcx(− √ ), 2 2 ∞ e− t 2 /2 u 1 2 √ eu /2 2π ∞ u 1 u dt = erfc( √ ) 2 2 e− t 2 /2 u 1 dt = erfcx( √ ). 2 2 8.10 Functions with bounded Newton decrement. Let f : Rn → R be a convex function with ∇2 f (x) ≻ 0 for all x ∈ dom f and Newton decrement bounded by a positive constant c: λ( x ) 2 ≤ c ∀x ∈ dom f. Show that the function g (x) = exp(−f (x)/c) is concave. 79 9 Interior point methods 9.1 Dual feasible point from analytic center. We consider the problem minimize f0 (x) subject to fi (x) ≤ 0, i = 1, . . . , m, (29) where the fu...
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