Reading List 2015.3.11 - Parallel variable distribution

• “Parallel variable distribution”

- Unconstrained parallel variable distribution;

- PVD with block separable constraints;

- PVD with general constraints: min f(x) such that g(x) <= 0;

  Handling inseparable constraints: exterior penalty[8], augmented Lagrangian methods[17], [3]. Avoid both of difficulties of above: the dual differentiable exact penalty function[10].

• “Parallel variable distribution for constrained optimization”

In parallel algorithms, an iteration consists of two steps: parallelization & synchronization[2].

Some methods: Block-Jacobi[2], updated conjugate subspaces[10], coordinate descent[21], parallel gradient distribution[14], PVD.

- Nonconvex separable constraints
- Convex inseparable constraints

• “On the Convergence of Constrained Parallel Variable Distribution Algorithms”

Also mentioned some methods: block Jacobi[2], coordinate descent[26], parallel gradient distribution algorithms[16].
Mainly prove the convergence of optimization problems with general convex constraints.