艳艳博客

Lipschitz gradientStrong continuousCo-coercivity of gradient1 Lipschitz of gradient2 Strong convex1. Lipschitz gradientIf ∇f(x)\nabla f(x) L-is lipschitz continuous, then we have 12L∥∇f(x)∥22≤f(x)

Properties of Proximal mapping1 L1 Lipschitz and monotone2 Projection Property3 Scaling and translation argument1. Properties of Proximal mappingFor a convex function h(x)h(x), its proximal mapping

gradient descent1 Model to consider2 Interpretaion21 Interpretation via newton method22 Interpretation via quadratic approximation of original function3 How to choose step size tktk4 Convergence

Proximal gradient descentExampleProperties of Proximal mapping1 Proximal gradient descentUnconstrained Problem with cost function split into two components. minf(x)=g(x)+h(x)\min f(x)=g(x)+h(x) whe

This is a short code for studying proximal gradient descent algorithm.#--------------------------- functions to be used ----------------------## the main function f = g + hf <- function(x, A, b, lambd

This is a short code for studying admm for lasso.#--------------------------- functions to be used ----------------------## the main function f = g + hf <- function(x, A, b, lambda){ 1/2*norm(