totsu

Totsu (凸 in Japanese) means convex.

This crate for Rust provides a basic primal-dual interior-point method solver: PDIPM.

Target problem

A common target problem is continuous scalar convex optimization such as LP, QP and QCQP. SOCP and SDP can also be handled with a certain effort.

Algorithm and design concepts

The overall algorithm is based on the reference: S. Boyd and L. Vandenberghe, "Convex Optimization", http://stanford.edu/~boyd/cvxbook/.

PDIPM has a core method solve which takes objective and constraint (derivative) functions as closures. Therefore solving a specific problem requires a implementation of those closures. You can use a pre-defined implementations (see predef), as well as construct a user-defined tailored version for the reason of functionality and efficiency.

This crate has no dependencies on other crates at all. Necessary matrix operations are implemented in mat and matsvd.

Example: QP

```rust use totsu::prelude::; use totsu::predef::;

let n: usize = 2; // x0, x1 let m: usize = 1; let p: usize = 0;

// (1/2)(x - a)^2 + const let matp = Mat::new(n, n).setiter(&[ 1., 0., 0., 1. ]); let vecq = Mat::newvec(n).set_iter(&[ -(-1.), // -a0 -(-2.) // -a1 ]);

// 1 - x0/b0 - x1/b1 <= 0 let matg = Mat::new(m, n).setiter(&[ -1. / 2., // -1/b0 -1. / 3. // -1/b1 ]); let vech = Mat::newvec(m).set_iter(&[ -1. ]);

let mata = Mat::new(p, n); let vecb = Mat::new_vec(p);

let param = PDIPMParam::default(); let rslt = PDIPM::new().solveqp(&param, &mut std::io::sink(), &matp, &vecq, &matg, &vech, &mata, &vec_b).unwrap();

let exp = Mat::newvec(n).setiter(&[ 2., 0. ]); println!("rslt = {}", rslt); assert!((&rslt - exp).norm_p2() < param.eps); ```

You can find other test examples of pre-defined solvers in lib.rs.