Manifold Sampling for ℓ1 Nonconvex Optimization

Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction.

Exploiting sparsity in the image gradient magnitude has proved to be an effective means for reducing the sampling rate in the projection view angle in computed tomography (CT). Most of the image reconstruction algorithms, developed for this purpose, solve a nonsmooth convex optimization problem involving the image total variation (TV). The TV seminorm is the ℓ1 norm of the image gradient magnit...

Manifold Sampling for Nonconvex Optimization of Piecewise Linear Compositions

We develop a manifold sampling algorithm for the unconstrained minimization of 4 a nonsmooth composite function f , ψ + h ◦ F when ψ is smooth with known derivatives, h is a 5 nonsmooth, piecewise linear function, and F is smooth but expensive to evaluate. The trust-region 6 algorithm classifies points in the domain of h as belonging to different manifolds and uses this knowl7 edge when computi...

An Efficient Neurodynamic Scheme for Solving a Class of Nonconvex Nonlinear Optimization Problems

‎By p-power (or partial p-power) transformation‎, ‎the Lagrangian function in nonconvex optimization problem becomes locally convex‎. ‎In this paper‎, ‎we present a neural network based on an NCP function for solving the nonconvex optimization problem‎. An important feature of this neural network is the one-to-one correspondence between its equilibria and KKT points of the nonconvex optimizatio...

Manifold Sampling for L1 Nonconvex Optimization

We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function h ◦ F . By classifying points in the domain of the nonsmooth function h into what we call manifolds, we adapt search directions within a trust-region framework based on knowledge of manifolds intersecting the current trust region. We motivate this idea through a study of l1...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients