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(Solved): Consider the following problem: Let \phi (x)=(1)/(2)||x||_(p)^(2) with p=(lnn)/(lnn-1). Prove that \ ...
Consider the following problem:
Let \phi (x)=(1)/(2)||x||_(p)^(2) with p=(lnn)/(lnn-1).
Prove that \phi (x) is (1)/(3lnn) - strongly convex with respect to ||*|| over R^(n), using
the definition of a strongly convex function.
2.1. Write down explicitly the Mirror-Descent method with \phi (x) as its mirror
map, for a convex minimization problem over an arbitrary convex and compact
set CsubeR^(n).
2.2 Let K be the number of iterations and denote by B_(\infty ) the upper-bound on
the l_(\infty ) norm of subgradients of f over C. Show that the rate of convergence of
the procedure in 2.1 is of the form O(RB_(\infty )\sqrt((lnn)/(K))), and give an expression to
R.