Proximal Distance Algorithms: Theory and Practice.

ABSTRACT: Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss f(x)+ρ2dist(x,C)2 and following the solution x _ρ to its limit as ρ tends to ∞. At each iteration the squared Euclidean distance dist(x,C)² is majorized by the spherical quadratic ‖x- P _C (x _k )‖², where P _C (x _k ) denotes the projection of the current iterate x _k onto C. The minimum

SUBMITTER: Keys KL 

PROVIDER: S-EPMC6812563 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature