Questions Tagged With non-smoothhttp://www.or-exchange.com/tags/non-smooth/?type=rssquestions tagged <span class="tag">non-smooth</span>enMon, 02 Mar 2015 15:58:02 -0500smoothing L1 normhttp://www.or-exchange.com/questions/11538/smoothing-l1-norm<p>Hi all,
How I could apply the L1 smoothing method for the following model: \[ \min \sum_i \alpha*(0.5 - | x_i - 0.5 |) \] where \(x \in [0,1]\) and \( \alpha >= 0 \)?</p>SaberMon, 02 Mar 2015 15:58:02 -0500http://www.or-exchange.com/questions/11538/smoothing-l1-normnonconvexoptimizationnon-smoothDecide whether a convex, non-differentiable function attaints its minimum at zerohttp://www.or-exchange.com/questions/11116/decide-whether-a-convex-non-differentiable-function-attaints-its-minimum-at-zero<p>Hi, what would be the best way (theoretically and practically) to decide whether a convex but (only) in 0 non-differentiable function attains its global minimum in zero? A possibility would be to use a subgradient method still needing the subgradients. Is there a way to easily test, if 0 is the global minimizer? For example, is it to easy decide if there is a point where 0 is in its subdifferential or to decide if no descent direction in this point exists? Is it sufficient to evaluate for example all points (0+e_i) and (0-e_i) for all unit vectors e_i and show that the objective function value is non-negative?</p>LongTue, 20 Jan 2015 09:05:14 -0500http://www.or-exchange.com/questions/11116/decide-whether-a-convex-non-differentiable-function-attaints-its-minimum-at-zeroglobal-optimizationoptimizationnon-smoothconvex