Description of graphsp_IP.m

>> out = graphsp_IP(Lp,E,Q,R,gamma,opts);

Matlab function graphsp_IP.m takes the problem data and the input opts and returns the solution to the sparsity-promoting optimal control problem (P). Input opts allows users to specify the following parameters

1. opts.eps_dg – tolerance on duality gap;

2. opts.eps_pres – tolerance on primal residual;

3. opts.maxit – maximum number of IP iterations;

4. opts.maxit_pcg – maximum number of PCG iterations;

5. opts.delta_pcg_aff – algorithm parameter for pcg method;

6. opts.delta_pcg – algorithm parameter for pcg method;

7. opts.method – method used for computing search directions.

If opts argument is omitted, the default values are set to:

1. opts.eps_dg = ;

2. opts.eps_pres = ;

3. opts.maxit = ;

4. opts.maxit_pcg = ;

5. opts.delta_pcg_aff = ;

6. opts.delta_pcg = ;

7. opts.method = 'pcg2’.

The output out is a structure that contains

1. out.x – optimal vector of the controller edge weights;

2. out.zp – optimal dual vector ;

3. out.zm – optimal dual vector ;

4. out.xp – optimal primal vactor ;

5. out.xm – optimal primal vector ;

6. out.dg – duality gap;

7. out.dres – dual residual;

8. out.pres – primal residual;

9. out.s – number of IP iterations;

10. out.ind1 – number of PCG iterations for affine search direction;

11. out.ind2 – number of PCG iterations for Mehrotra search direction.

Description of graphsp_proxBB.m

>> out = graphsp_proxBB(Lp,E,Q,R,gamma,opts);

Matlab function graphsp_proxBB.m takes the problem data and the input opts and returns the solution to the sparsity-promoting optimal control problem (P). Input opts allows users to specify the following parameters

1. opts.eps_dg - tolerance on duality gap;

2. opts.eps_pres - tolerance on primal residual;

3. opts.eps_res - tolerance on dual residual;

4. opts.maxit - maximum number of IP iterations;

5. opts.flagBB - flag for BB step-size initialization.

If opts argument is omitted, the default values are set to:

1. opts.eps_dg = ;

2. opts.eps_pres = ;

3. opts.eps_dres = ;

4. opts.maxit = ;

5. opts.flagBB = .

The output out is a structure that contains

1. out.x - optimal vector of edge weights;

2. out.s - number of proxBB iterations;

3. out.dg - duality gap;

4. out.pres - primal residual;

5. out.dres - dual residual;

6. out.ss - step-size;

7. out.js - number of iterations for line-search;

8. out.iter_time - time of an inner iteration.

Description of graphsp_proxN.m

>> out = graphsp_proxN(Lp,E,Q,R,gamma,opts);

Matlab function graphsp_proxN.m takes the problem data and the input opts and returns the solution to the sparsity-promoting optimal control problem (P). Input opts allows users to specify the following parameters

1. opts.eps_dg - tolerance on duality gap;

2. opts.eps_pres - tolerance on primal residual;

3. opts.eps_res - tolerance on dual residual;

4. opts.maxit - maximum number of IP iterations.

If opts argument is omitted, the default values are set to:

1. opts.eps_dg = ;

2. opts.eps_pres = ;

3. opts.eps_dres = ;

4. opts.maxit = .

The output out is a structure that contains

1. out.x - optimal vector of edge weights;

2. out.s - number of proxBB iterations;

3. out.dg - duality gap;

4. out.pres - primal residual;

5. out.dres - dual residual;

6. out.ss - step-size;

7. out.js - number of iterations for line-search;

8. out.iter_time - time of an inner iteration.

Description of run_graphsp_IP.m

>> run_graphsp_IP;

Matlab script run_graphsp_IP.m allows users to:

• call graphsp_IP.m.

Please set flag_p to:

• 1 – for Erdos-Renyi plant network;

• 1 – for path plant network;

• 2 – for a randomly generated disconnected network with nodes.

run_graphsp_IP.m gives:

1. (output of graphsp_IP.m for opts.method = 'chol’) and (total running time);

2. (output of graphsp_IP.m for opts.method = 'pcg1’) and (total running time);

3. (output of graphsp_IP.m for opts.method = 'pcg2’) and (total running time).

Description of run_graphsp_IP.m

>> run_graphsp;

Matlab script run_graphsp.m allows users to:

• call graphsp.m.

Please set flag_p to:

• 1 – for Erdos-Renyi plant network;

• 1 – for path plant network;

• 2 – for a randomly generated disconnected network with nodes.

run_graphsp_IP.m gives:

1. (output of graphsp_IP.m for opts.method = 'chol’) and (total running time);

2. (output of graphsp_IP.m for opts.method = 'pcg1’) and (total running time);

3. (output of graphsp_IP.m for opts.method = 'pcg2’) and (total running time);

4. (output of graphsp_proxBB.m for proxBB) and (total running time);

5. (output of graphsp_proxN.m for proxN) and (total running time);