https://github.com/simon-lc/mehrotra.jl

Solver for complemetarity-based dynamics.
https://github.com/simon-lc/mehrotra.jl

Last synced: about 1 month ago
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Solver for complemetarity-based dynamics.

• Host: GitHub
• URL: https://github.com/simon-lc/mehrotra.jl
• Owner: simon-lc
• License: mit
• Created: 2022-05-01T03:50:28.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-12-17T10:30:57.000Z (about 2 years ago)
• Last Synced: 2024-11-09T21:58:33.168Z (about 2 months ago)
• Language: Julia
• Size: 944 KB
• Stars: 7
• Watchers: 3
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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# Mehrotra.jl

A solver for cone-constrained feasibility problems. The main application for this solver is implicit integration of contact dynamics.

## Standard form

Problems of the following form:

```

find         x = [y, z, s]

subject to   f(y,z,s; p) = 0,

             z ∘ s = κ

             z, s in K = R+ x Q^1 x ... x Q^k

```

can be optimized for

- x = [y, z, s]: decision variables

- y: primal variables

- z: dual variables

- s: slack variables

- p: problem parameters

- κ: central-path parameter

- ∘: cone product

- K: Cartesian product of convex cones; nonnegative orthant R+ and second-order cones Q are currently implemented

## Solution gradients

The solver is differentiable, and gradients of the solution (including internal solver variables) with respect to the problem parameters are efficiently computed.

## Quick start

```julia

using Mehrotra

```

## Remaining tasks

- [ ] @turbo loop vectorization

- [ ] in-place addition to a vector using symbolics

- [ ] sparse allocation-free linear solve

- [ ] warm-starting strategy (add user-provided slacks initialization method s = F(z) in general)

- [x] consistency logic for efficient dynamics query

- [ ] exploit structure of the symmetric problems

- [x] allocation-free implementation

- [ ] experiment with different relaxation scheduling strategies

- [ ] add documentation

- [ ] register package