qics.Model

class qics.Model(c, A=None, b=None, G=None, h=None, cones=None, offset=0.0)

A class representing an instance of the standard form primal

\[ \begin{align}\begin{aligned}\min_{x \in \mathbb{R}^n} &&& c^\top x\\\text{s.t.} &&& b - Ax = 0\\ &&& h - Gx \in \mathcal{K},\end{aligned}\end{align} \]

and dual

\[ \begin{align}\begin{aligned}\max_{y \in \mathbb{R}^p, z \in \mathbb{R}^q} &&& -b^\top y - h^\top z\\\text{s.t.} &&& c + A^\top y + G^\top z = 0\\ &&& z \in \mathcal{K}_*,\end{aligned}\end{align} \]

conic programs, where \(c\in\mathbb{R}^n\), \(b\in\mathbb{R}^p\), \(h\in\mathbb{R}^q\), \(A\in\mathbb{R}^{p\times n}\), \(G\in\mathbb{R}^{q\times n}\), and \(\mathcal{K}\subset\mathbb{R}^{q}\) is a convex, proper cone with dual cone \(\mathcal{K}_*\subset\mathbb{R}^{q}\).

Parameters:

cndarray

2D float64 array of size (n, 1) representing the linear objective \(c\).

Andarray or sparray, optional

2D float64 array of size (p, 1) representing linear equality constraint matrix \(A\). The default is numpy.empty((0, n)), i.e., there are no linear equalitiy constraints.

bndarray, optional

2D float64 array of size (p, 1) representing linear equality constraint vector \(b\). The default is numpy.zeros((p, 1)), i.e., \(b=0\).

Gndarray or sparray, optional

2D float64 array of size (q, n) representing linear cone constraint matrix \(G\). The default is -scipy.sparse.eye(n), i.e., cone constraints are of the simplified form \(x+h\in\mathcal{K}\).

hndarray, optional

2D float64 array of size (q, 1) representing linear cone constraint vector \(h\). The default is numpy.zeros((q, 1)), i.e., \(h=0\).

coneslist of cones, optional

Cartesian product of cones \(\mathcal{K}\). Default is [] i.e., there are no conic constraints.

offsetfloat, optional

Constant offset term to add to the objective function. Default is 0.