An open source first-order MATLAB solver for conic programs with row sparsity. SOSADMM implements the alternating direction method of multipliers (ADMM) described in our paper

• Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programs using ADMM (included in the doc/ folder)

In particular, SOSADMM exploits the sparsity of the coefficient matching conditions when SOS programs are formulated in the usual monomial basis to reduce the computational costs of the ADMM algorithm (see the detailed descriptions in our paper).

SOSADMM solves in the standard SDP in the primal vectorized form

	minimize 	c'x						
(1)	subject to	Ax = b,					
			x \in K							

SOSADMM supports cartesian products of the following cones:

• R^n (free variables)
• Non-negative orthant
• Second-order cone
• Positive semidefinite cone

SOSADMM is called with the syntax

>> [x,y,z,info] = sosadmm(At,b,c,K,options);

where At is the transpose of the matrix A in problem (1) above. Note that the inputs and outputs are in the same format used by SeDuMi.

To contact us about SOSADMM, suggest improvements and report bugs, please feel free to email Yang Zheng or Giovanni Fantuzzi.

If you find SOSADMM useful, please cite the following paper:

@article{{ZFP2017,
    archivePrefix= {arXiv},
    eprint       = {arXiv:1703.01969},
    primaryClass = "math-OC",
    author       = {Zheng, Yang and Fantuzzi, Giovanni and Papachristodoulou},
    title        = {Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programming using {ADMM}}
    }