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Unformatted text preview: EE364b Prof. S. Boyd EE364b Homework 2 1. Subgradient optimality conditions for nondifferentiable inequality constrained optimiza- tion. Consider the problem minimize f ( x ) subject to f i ( x ) , i = 1 , . . ., m, with variable x R n . We do not assume that f , . . ., f m are convex. Suppose that x and followsequal 0 satisfy primal feasibility, f i ( x ) , i = 1 , . . ., m, dual feasibility, f ( x ) + m summationdisplay i =1 i f i ( x ) , and the complementarity condition i f i ( x ) = 0 , i = 1 , . . ., m. Show that x is optimal, using only a simple argument, and definition of subgradient. Recall that we do not assume the functions f , . . ., f m are convex. 2. Optimality conditions and coordinate-wise descent for 1-regularized minimization. We consider the problem of minimizing ( x ) = f ( x ) + bardbl x bardbl 1 , where f : R n R is convex and differentiable, and 0. The number is the regularization parameter, and is used to control the trade-off between small...
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This note was uploaded on 04/09/2010 for the course EE 360B taught by Professor Stephenboyd during the Fall '09 term at Stanford.
- Fall '09