Skoltech, October 10, 2016
Problems for the mini-course
Basics of optimization
Kabatyansky G.A., Gasnikov A.V.
Problem 1 (Lagrange multipliers principle and Implicit function theorem, 1.0). We
have a sufficiently smooth optimization
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Statistics mini-course HW
due to 20 October, 23:59
Problem 1 Consider two independent observations of a random variable:
x1 = 0.2
x2 = 0.3
Find the most powerful test for which the first kind of error is less than = 0.0314 for two following simple
Problem 1 (censored data fitting) cens_fit_data.m, 2 points (additional exercise A5.13 to
Boyd and Vandenberghe).
Problem 2 (vehicle speed scheduling) veh_speed_sched_data.m, 3 points (additional
exercise A3.20 to Boyd and Vandenberghe). This is the same
Graphs and algorithms HW
Due to 9:00 14.10.16
Formulate min-cut problem on graphs in terms
of convex optimization problem. Proof the
Provide an efficient implimentation of queue
using stack or arrays or doubly linked lists.
Estimate the wor
Skoltech, October 17, 2016
Problems for the mini-course Probability theory
Kabatyansky G.A., Gasnikov A.V. [email protected]
Problem 1 (Random walk, 1.5). There is a point on one-dimensional integer lattice Z.
With probability 0.5 the point moves to t
u = f (t),
t = t(x, y)
t = t(x, y) u = f (t(x, y) u v u0x u0y .
u0x = ft0 t0x ,
u0y = ft0 t0y
z = z(x, y),
x = x(t),
y = y(t)
x = x(t) y = y(t) z = z(x(t), y(t) t zt0 .
zt0 = zx0 x0t +