# Checklist

09 Nov 2016## 1. The Problems.

Each problem must eventually be cast as a feasibility problem. In particular, the feasibility problem must be cast as finding a point in the intersection of an affine set and a cone. Note that the cone, however, may be the cross-product of multiple different cones.

## 2. + 3. The Algorithms

.

Alternating projections

Dykstra’s

ADMM

Halfspace Eliminating Alternating Projections (memory )

Halfspace Eliminating Alternating Projections (memory )

Halfspace Eliminating Alternating Projections, with momentum

Halfspace Eliminating Alternating Projections, with plane search / momentum

Halfspace Eliminating Alternating Projections, with plane search / momentum and additional problem transformations

## 4. Theoretical Analyses

Halfspace Eliminating Alternating Projections (free, from Pang)

Halfspace Eliminating Alternating Projections, with plane search

Halfspace Eliminating Alternating Projections, with plane search and additional problem transformations

## 5. The Test Cases

2D feasibility problems, for intuition’s sake.

Intersection of second-order cone and affine set, randomly generated

Random cone problems of varying sizes.

- NB: Can use the method described in the long SCS paper to generate these problems. Will need to take generated problem and form the self-dual homogeneous embedding in order to recover the feasibility problem, however.

Open test suite for feasibility problems?

- To the best of my knowledge, none exist!