Slope-adaptive Variable Selection via Convex Optimization.

Group SLOPE – Adaptive Selection of Groups of Predictors

Sorted L-One Penalized Estimation (SLOPE, [10]) is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. This approach is particularly useful when variables in ...

Slope—adaptive Variable Selection via Convex Optimization by Małgorzata Bogdan∗,1, Ewout

min b∈Rp 1 2 ‖y −Xb‖2 2 + λ1|b|(1) + λ2|b|(2) + · · · + λp|b|(p), where λ1 ≥ λ2 ≥ · · · ≥ λp ≥ 0 and |b|(1) ≥ |b|(2) ≥ · · · ≥ |b|(p) are the decreasing absolute values of the entries of b. This is a convex program and we demonstrate a solution algorithm whose computational complexity is roughly comparable to that of classical 1 procedures such as the Lasso. Here, the regularizer is a sorted 1 ...

Rejoinder: Latent Variable Graphical Model Selection via Convex Optimization by Venkat Chandrasekaran,

Slope Stability Analysis Using a Self-Adaptive Genetic Algorithm

This paper introduces a methodology for soil slope stability analysis based on optimization, limit equilibrium principles and method of slices. In this study, the slope stability analysis problem is transformed into a constrained nonlinear optimization problem. To solve that, a Self-Adaptive Genetic Algorithm (GA) is utilized. In this study, the slope stability safety factors are the objective ...

Faster Coordinate Descent via Adaptive Importance Sampling

Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive, we mean that our selection rules are based on the dual residual or the primal-dual gap estimates and can change at each iteration. We theoretically character...