DESP (version 0.1-2)

scsSOCP: solve a second-order cone program using SCS

Description

This function solves a second-order cone program using the C package SCS that solves convex cone problems via operator splitting. We use the direct method of the C package SCS that also proposes an indirect method. This method solves an optimization problem of the form : minimize c^T x subject to b - A x = s, s in K, where K is a product of zero, linear and second-order cones, containing the following informations (in this order) : f : number of linear equality constraints, l : length of LP cone, q : array of second-order cone constraints, qsize : length of SOC array (number of second-order cones).

Usage

scsSOCP(model)

Arguments

model

The model representing the convex problem to solve is a list containing the components that follow. The sparse matrix A is stored using the compressed sparse column (CSC) format. [object Object],[object Object],[object Object],[object Object],[object

Value

• scsSOCP returns a list containing the optimal solution, with components:
• x
  The value of the primal variable for the best solution.
• status
  The status of the optimization, returned as an integer : 1 in case of a solved program. A negative status corresponds to an infeasible, unbounded, inaccurate, interrupted, failed or indeterminate problem. Refer to the SCS development pages for more documentation on status codes.

Details

More documentation on SCS can be found at https://github.com/cvxgrp/scs.

References

O'Donoghue, B. and Chu, E. and Parikh, N. and Boyd, S. (2015): Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding.