# Crate totsu_core

Expand description

Totsu ( in Japanese) means convex.

This crate for Rust provides a first-order conic linear program solver for convex optimization.

## Target problem

A common target problem is continuous scalar convex optimization such as LP, QP, QCQP, SOCP and SDP. Each of those problems can be represented as a conic linear program: $\begin{array}{ll} {\rm minimize} & c^T x \\ {\rm subject \ to} & A x + s = b \\ & s \in \mathcal{K}, \end{array}$ where

• variables $$x \in \mathbb{R}^n,\ s \in \mathbb{R}^m$$
• $$c \in \mathbb{R}^n$$ as an objective linear operator
• $$A \in \mathbb{R}^{m \times n}$$ and $$b \in \mathbb{R}^m$$ as constraint linear operators
• a nonempty, closed, convex cone $$\mathcal{K}$$.

## Algorithm and design concepts

The author combines the two papers [1] [2] so that the homogeneous self-dual embedding matrix in [2] is formed as a linear operator in [1].

A core method solver::Solver::solve takes the following arguments:

Therefore solving a specific problem requires an implementation of those traits. You can use pre-defined implementations: totsu crate, as well as construct a user-defined tailored version for the reason of functionality and efficiency. This crate also contains several basic structs that implement solver::Operator and solver::Cone trait.

Core linear algebra operations that solver::Solver requires are abstracted by solver::LinAlg trait, while subtrait LinAlgEx is used for the basic structs. This crate contains a LinAlgEx implementor:

Other crates are also available:

## Features

This crate can be used without the standard library (#![no_std]). Use this in Cargo.toml:

[dependencies.totsu_core]
version = "0.*"
default-features = false
features = ["libm"]


## References

1. T. Pock and A. Chambolle. “Diagonal preconditioning for first order primal-dual algorithms in convex optimization.” 2011 International Conference on Computer Vision. IEEE, 2011.
2. B. O’donoghue, et al. “Conic optimization via operator splitting and homogeneous self-dual embedding.” Journal of Optimization Theory and Applications 169.3 (2016): 1042-1068.
3. N. Parikh and S. Boyd. “Proximal algorithms.” Foundations and Trends in optimization 1.3 (2014): 127-239.
4. Mosek ApS. “MOSEK modeling cookbook.” (2020).
5. S. Boyd and L. Vandenberghe. “Convex Optimization.” (2004).

## Modules

First-order conic linear program solver

## Macros

Splits a SliceRef into multiple ones.
Splits a SliceMut into multiple ones.

## Structs

Positive semidefinite cone
Nonnegative orthant cone
num::Float-generic LinAlgEx implementation