YALL1-Group: A solver for group/joint sparse reconstruction

From Wikimization

(Difference between revisions)
Jump to: navigation, search
(Syntax)
Line 24: Line 24:
== Input Description ==
== Input Description ==
-
* '''c''': objective coefficient vector, double type.
 
-
:[] (empty array) means uniformly <font face="Times">0</font> coefficients, and ''scalar'' means all coefficients equal to ''scalar''.
 
-
* '''objtype''': 1 (minimization) or -1 (maximization).
 
-
* '''A''': constraint coefficient matrix, double type, sparse.
 
-
* '''b''': constraint right-hand side vector, double type.
 
-
:Gurobi takes a dense vector for this input. If a ''sparse'' vector is specified, it will be converted to ''full'' by Gurobi Mex.
 
-
* '''contypes''': constraint types. Char array of '>', '<', '='.
 
-
:Warning: '>=' specifies two constraints, not one.
 
-
:Example: '>><=' specifies four constraints. The first two constraints have ''greater or equal to'' signs, the third has ''less than or equal to'' sign, and the last is an equality constraint.
 
-
:If a single character is specified, all constraints have the corresponding type uniformly.
 
-
* '''lb''': variable lower bound, double type, either scalar or vector.
 
-
:[] (empty array) means <font face="Times">0</font> lower bound. -inf means no lower bound. If a scalar is specified, it will be the uniform lower bound for all variables.
 
-
* '''ub''': variable upper bound, double type, either scalar or vector.
 
-
:[] (empty array) means no (or infinity) upper bound. If a scalar is specified, it will be the uniform upper bound for all variables.
 
-
* '''vartypes''': variable types, char array of 'C', 'B', 'I', 'S', 'N'. 'C' for continuous; 'B' for binary; 'I' for integer; 'S' for semi-continuous; 'N' for semi-integer. [] (empty array) means all variables are continuous.
 
-
:Example: 'CCCCC' specifies five continuous variables.
 
-
:Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero.
 
-
Semi-integer variables are similarly defined.
 
-
:If a single character is specified, all variables will be signed to the corresponding type uniformly.
 
-
=== [http://www.gurobi.com/doc/40/refman/node572.html Gurobi Parameters] ===
 
-
* '''opts''': optional structure that may have any number of following parameters.
 
-
** '''opts.[any Gurobi parameter]''': See [http://www.gurobi.com/doc/40/refman/node572.html Gurobi Parameters] for their allowed values.
 
-
** '''opts.QP''': Quadratic objective terms. See [http://www.convexoptimization.com/wikimization/index.php/Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#Quadratic_Programming here].
 
-
** '''opts.SOS''': Special ordered set constraints. See [http://www.convexoptimization.com/wikimization/index.php/Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#SOS_Constraints here].
 
-
** '''opts.Start''': MIP start vector, or Gurobi's attribute 'Start'. See [http://www.convexoptimization.com/wikimization/index.php/Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#MIP_Start_Vector here].
 
-
** '''opts.TrapCtrlC''': true (to trap Ctrl-C) or false (not to trap Ctrl-C).
 
-
** '''opts.Display''': screen output level. <font face="Times">0</font> (no output); 1 (error only); 2 (default output). For complete silence, set '''opts.DisplayInterval=<font face="Times">0</font>''' and '''opts.OutputFlag=<font face="Times">0</font>''' (to silence Gurobi) and '''opts.Display=<font face="Times">0</font>''' (to make Gurobi Mex silent).
 
-
** '''opts.WriteToFile''': char array of the name of the file to which optimization data is written. See Gurobi C-Reference entry [http://www.gurobi.com/doc/40/refman/node39.html GRBwrite] for supported formats. This option helps one verify whether the model is correctly passed to Gurobi.
 
- 
-
== Output Description ==
 
-
* '''x''': primal solution vector; empty if Gurobi encounters errors or stops early (in this case, check output flag).
 
-
* '''val''': optimal objective value; empty if Gurobi encounters errors or stops early.
 
-
* '''flag''': value meanings:
 
-
** [ ] (empty 1x1 array) general failure
 
-
** 1 for not started
 
-
** 2 for optimal
 
-
** 3 for infeasible
 
-
** 4 for infeasible or unbounded
 
-
** 5 for unbounded
 
-
** 6 for objective worse than user-specified cutoff
 
-
** 7 for reaching iteration limit
 
-
** 8 for reaching node limit
 
-
** 9 for reaching time limit
 
-
** 10 for reaching solution limit
 
-
** 11 for user interruption
 
-
** 12 for numerical difficulties
 
-
** 13 for suboptimal solution ('''Gurobi 3''' and later)
 
-
* '''output''': structure contains the following fields
 
-
** '''output.IterCount''': number of Simplex iterations
 
-
** '''output.Runtime''': running time in seconds
 
-
** '''output.ErrorMsg''': contains Gurobi error message, if any
 
-
* '''lambda''': Lagrange multipliers. Because solving MIPs gives no such output, ''do not'' ask for this output for MIPs.
 
- 
-
== Notes ==
 
-
=== Quadratic Programming ===
 
-
'''Gurobi 4''' and later solve quadratic programs. The quadratic terms in the objective function should be specified by '''opts.QP.qrow''', '''opts.QP.qcol''', and '''opts.QP.qval''', which correspond to the input arguments ''qrow'', ''qcol'', and ''qval'' of [http://gurobi.com/doc/40/refman/node11.html function GRBaddqpterms]. They are all 1D arrays. The first two arguments, ''qrow'' and ''qcol'', specify the row and column indices (starting from 0) of 2nd-order terms such as <math>x_1^2</math> and <math>x_1 x_2\,</math>. The third argument, ''qval'', gives their coefficients. An example is given [http://www.convexoptimization.com/wikimization/index.php/Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#Example_5._Quadratic_programming below].
 
- 
-
----
 
- 
-
=== SOS Constraints ===
 
-
SOS stands for [http://www.google.com/search?q=special+ordered+set+SOS Special Ordered Sets]. This mex program uses opts.SOS.weights and opts.SOS.types to pass SOS constraints to Gurobi. '''opts.SOS.weights''' is a ''sparse'' matrix describing the weights of SOS variables, and '''opts.SOS.types''' a 1D array of type int32 or int64 (if sizeof(int) is 4 for your system, then you should use int32; if 8, use int64), which specifies the constraint types. Here is an example with 4 variables and 3 SOS constraints:
 
- 
-
SOS1: x1 = 0 or x2 = 0
 
-
SOS1: x1 = 0 or x3 = 0
 
-
SOS2: (x1, x3, x2, x4)
 
- 
-
The corresponding code for a 32-bit system is
 
-
opts.SOS.weights = sparse([
 
-
1 1 1;
 
-
2 0 3;
 
-
0 2 2;
 
-
0 0 4]);
 
-
opts.SOS.types = int32([1 1 2]);
 
-
The ''i''th column of '''opts.SOS.weights''' specifies the weights (i.e., orders) of the variables in the ''i''th SOS constraint.
 
- 
-
----
 
- 
-
=== MIP Start Vector ===
 
-
To specify an MIP start vector (supported since v1.45), say x = [1 0 3 2], one can use one of the following two ways:
 
- 
-
opts.Start = [1 0 3 2];
 
- 
-
or
 
- 
-
opts.Start.pos = int32([0 1 2 3]); % use int64 if sizeof(int) is 8 for your system
 
-
opts.Start.val = [1 0 3 2];
 
- 
-
To specify start values for a subset of variables, for example to set x = [? ? -1 2], where ? means undefined, one can choose either one of the following two ways
 
- 
-
GRB_UNDEFINED = 1e101;
 
-
opts.Start = [GRB_UNDEFINED GRB_UNDEFINED -1 2];
 
- 
-
or
 
- 
-
opts.Start.pos = int32([2 3]); % use int64 if sizeof(int) is 8 for your system
 
-
opts.Start.val = [-1 2];
 
- 
-
----
 
- 
-
=== How to pass a parameter from MATLAB to Gurobi? ===
 
-
v1.35 and v1.45 support all parameters of '''Gurobi 3''' and '''4''', respectively. However, if you want to specify a new or undocumented Gurobi parameter of your interest, you can DIY very easily. Suppose that we want to set a double-type parameter called '''SecretPara''' in MATLAB and pass it through this mex interface to Gurobi. Because the parameter '''TimeLimit''' has the same (double) type and it is already supported by this mex program, we can copy the code for '''TimeLimit''', replace TimeLimit by SecretPara in the code, and paste it at Line 1250 of v1.35 (or Line 510 of v1.30), just before the mex program checks unrecognized input option fields. After compiling ''gurobi.c'', the modified mex will let you assign a double value to '''opts.SecretPara'''. We compare the code for '''TimeLimit''' and '''SecretPara''' below where the differences are italicized:
 
- 
-
/* Option ''TimeLimit'' */
 
-
field_n = mxGetFieldNumber(IN_OPTS, "''TimeLimit''");
 
-
if (field_n != -1) {
 
-
field = mxGetFieldByNumber(IN_OPTS,0,field_n);
 
-
bOpts[field_n] = true;
 
-
if (!mxIsDouble(field) || mxIsComplex(field) || mxIsEmpty(field)) {
 
-
mexPrintf("''Option TimeLimit must be real positive double (0 to inf).''");
 
-
goto QUIT;
 
-
}
 
-
error = GRBsetdblparam(env, "''TimeLimit''", mxGetScalar(field));
 
-
if (error) goto QUIT;
 
-
}
 
- 
-
/* Option ''SecretPara'' */
 
-
field_n = mxGetFieldNumber(IN_OPTS, "''SecretPara''");
 
-
if (field_n != -1) {
 
-
field = mxGetFieldByNumber(IN_OPTS,0,field_n);
 
-
bOpts[field_n] = true;
 
-
if (!mxIsDouble(field) || mxIsComplex(field) || mxIsEmpty(field)) {
 
-
mexPrintf("''Option SecretPara must real double (?? through ??).''");
 
-
goto QUIT;
 
-
}
 
-
error = GRBsetdblparam(env, "''SecretPara''", mxGetScalar(field));
 
-
if (error) goto QUIT;
 
-
}
 
- 
-
Note that you must start from a parameter of the ''same'' type (int, double, or string). In case memory allocation is needed, use ''mxCalloc'' and make sure that ''mxFree'' has been called whenever the mex program exits, normally or not.
 
- 
-
== Callbacks ==
 
-
Callbacks are useful to obtain the progress of Gurobi (e.g., by calling GRBcbget) and to modify its behavior during runtime (e.g., by calling GRBcbcut and GRBcbsolution).
 
- 
-
Gurobi Mex implements a callback function ''mycallback'' to obtain Gurobi's progress messages and print them on the MATLAB screen. The print frequency is set in '''opts.DisplayInterval''' (in seconds). The same function is also used to detect user input Ctrl-C.
 
- 
-
Information for Gurobi callbacks can be found [http://www.gurobi.com/doc/40/refman/node84.html here] in Gurobi's help. An example can be found [http://www.gurobi.com/doc/40/examples/node8.html here].
 
- 
-
== Examples ==
 
- 
-
=== Example 1. Linear programming ===
 
-
This example is borrowed from MATLAB's linprog help.
 
- 
-
Problem:
 
-
<pre>
 
-
min –5 x1 – 4 x2 –6 x3,
 
- 
-
subject to
 
-
x1 – x2 + x3 ≤ 20
 
-
3 x1 + 2 x2 + 4 x3 ≤ 42
 
-
3 x1 + 2 x2 ≤ 30
 
-
0 ≤ x1, 0 ≤ x2, 0 ≤ x3.
 
-
</pre>
 
-
MATLAB code:
 
-
<pre>
 
-
c = [-5; -4; -6];
 
-
objtype = 1;
 
-
A = sparse([1 -1 1; 3 2 4; 3 2 0]);
 
-
b = [20; 42; 30];
 
-
lb = zeros(3,1); % same as lb = [];
 
-
ub = [];
 
-
contypes = '<<<';
 
-
vtypes = []; % same as vtypes = 'CCC'; [] means 'C...C'
 
- 
-
clear opts
 
-
opts.IterationLimit = 20;
 
-
opts.FeasibilityTol = 1e-6;
 
-
opts.IntFeasTol = 1e-5;
 
-
opts.OptimalityTol = 1e-6;
 
-
opts.Method = 1; % 0 - primal, 1 - dual
 
-
opts.Presolve = -1; % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
 
-
opts.Display = 1;
 
-
opts.LogFile = 'test_gurobi_mex_LP.log'; % optional
 
-
opts.WriteToFile = 'test_gurobi_mex_LP.mps'; % optional; it can cause a long delay if problem is large
 
- 
-
[x,val,exitflag,output,lambda] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
 
-
</pre>
 
-
Results:
 
-
<pre>
 
-
x' =
 
-
0 15 3
 
- 
-
val =
 
-
-78
 
- 
-
exitflag =
 
-
2
 
- 
-
output =
 
-
IterCount: 2
 
-
Runtime: 0
 
-
ErrorMsg: []
 
- 
-
lambda' =
 
-
0 -1.5000 -0.5000
 
-
</pre>
 
-
Log file: ''test_gurobi_mex_LP.log''. MPS file: ''test_gurobi_mex_LP.mps''.
 
- 
-
=== Example 2. Integer programming ===
 
-
This example is borrowed from ''mip1_c.c'' of '''Gurobi 2'''.
 
- 
-
Problem:
 
-
<pre>
 
-
max x + y + 2z,
 
- 
-
subject to
 
-
x + 2 y + 3 z <= 4
 
-
x + y >= 1
 
-
x, y, z binary.
 
-
</pre>
 
-
MATLAB code:
 
-
<pre>
 
-
c = [1; 1; 2];
 
-
objtype = -1; % 1 for minimize, -1 for maximize
 
-
A = sparse([1 2 3; 1 1 0]);
 
-
b = [4; 1];
 
-
lb = [];
 
-
ub = [];
 
-
contypes = '<>';
 
-
vtypes = 'BBB';
 
- 
-
clear opts
 
-
opts.IterationLimit = 20;
 
-
opts.FeasibilityTol = 1e-6;
 
-
opts.IntFeasTol = 1e-5;
 
-
opts.OptimalityTol = 1e-6;
 
-
opts.Method = 1; % 0 - primal, 1 - dual
 
-
opts.Presolve = -1; % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
 
-
opts.Display = 1;
 
-
opts.LogFile = 'test_gurobi_mex_MIP.log';
 
-
opts.WriteToFile = 'test_gurobi_mex_MIP.mps'; % this option can cause a long delay if problem is large
 
- 
-
[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
 
-
</pre>
 
-
Gurobi does not give lambda (Pi, or Lagrange multipliers) for MIPs, unless model fix is called.
 
- 
-
Results:
 
-
<pre>
 
-
disp('Solution:');disp(x')
 
-
disp('Optimal obj value:');disp(val)
 
-
disp('Exit flag:');disp(exitflag)
 
-
disp('Optimization info:');disp(output)
 
- 
-
Solution:
 
-
1 0 1
 
- 
-
Optimal obj value:
 
-
3
 
- 
-
Exit flag:
 
-
2
 
- 
-
Optimization info:
 
-
IterCount: 0
 
-
Runtime: 0
 
-
ErrorMsg: []
 
-
</pre>
 
-
Log file: ''test_gurobi_mex_MIP.log''. MPS file: ''test_gurobi_mex_MIP.mps''.
 
- 
-
=== Example 3. Feasibility test ===
 
-
Problem:
 
-
<pre>
 
-
Find a solution or report infeasibility of
 
- 
-
5 x1 + 4 x2 + 5 x4 >= -21
 
-
5 x1 + 3 x2 + 1 x3 + 4 x4 = -14
 
-
3 x1 + 5 x2 + 2 x3 - 5 x4 = 11
 
-
x1,x2,x3,x4 >= 0.
 
-
</pre>
 
-
MATLAB code:
 
-
<pre>
 
-
c = []; % use [] or 0 for null objective
 
-
objtype = -1; % 1 for minimize, -1 for maximize
 
-
A = sparse([5 4 0 5; 5 3 1 4; 3 5 2 -5]);
 
-
b = [-21; -14; 11];
 
-
lb = []; % stands for 0 lower bound uniformly
 
-
ub = []; % stands for inf upper bound uniformly
 
-
contypes = '>==';
 
-
vtypes = []; % same as vtypes = 'CCCC'
 
- 
-
clear opts
 
-
opts.FeasibilityTol = 1e-6;
 
-
opts.Presolve = -1; % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
 
-
opts.Display = 1;
 
-
opts.LogFile = 'test_gurobi_mex_Feasibility.log';
 
-
opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps'; % this option can cause a long delay if problem is large
 
- 
-
[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
 
-
</pre>
 
- 
-
Results:
 
-
<pre>
 
-
disp('Solution:');disp(x')
 
-
disp('Optimal obj value:');disp(val)
 
-
disp('Exit flag:');disp(exitflag)
 
- 
-
Model is infeasible. No solution will be returned.
 
- 
-
Solution:
 
-
Optimal obj value:
 
-
Exit flag:
 
-
3
 
-
</pre>
 
-
Log file: ''test_gurobi_mex_Feasibility.log''. MPS file: ''test_gurobi_mex_Feasibility.mps''.
 
- 
-
=== Example 4. SOS constraint test ===
 
-
Problem:
 
-
<pre>
 
-
min –3 x1 – 1 x2 – 1 x3,
 
- 
-
subject to
 
-
x1 + x2 + x3 <= 2,
 
-
0 <= x1 <= 1, 0 <= x2 <= 1, 0 <= x3 <= 2,
 
-
SOS type 1: x1 = 0 or x2 = 0,
 
-
SOS type 1: x1 = 0 or x3 = 0.
 
-
</pre>
 
-
MATLAB code:
 
-
<pre>
 
-
c = [-3; -1; -1];
 
-
objtype = 1;
 
-
A = sparse([1 1 1]);
 
-
b = 2;
 
-
lb = []; % means 0 lower bound
 
-
ub = [1 1 2];
 
-
contypes = '<';
 
-
vtypes = []; % same as vtypes = 'CCC'
 
-
sos.weights = sparse([1 1; 2 0; 0 2]);
 
-
sos.types = int32([1 1]); % Both the SOS constraints are of type 1
 
- 
-
clear opts
 
-
opts.FeasibilityTol = 1e-6;
 
-
opts.Presolve = -1; % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
 
-
opts.Display = 1;
 
-
opts.LogFile = 'test_gurobi_mex_Feasibility.log';
 
-
opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps';
 
- 
-
[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
 
-
</pre>
 
- 
-
Results:
 
-
<pre>
 
-
Optimal solution found (tolerance 1.00e-04)
 
-
Best objective -3.0000000000e+00, best bound -3.0000000000e+00, gap 0.0%
 
-
 
-
Solution:
 
-
1 0 0
 
-
</pre>
 
-
Log file: ''test_gurobi_mex_SOS.log''. MPS file: ''test_gurobi_mex_SOS.mps''.
 
- 
-
=== Example 5. Quadratic programming ===
 
-
This example appears in MATLAB Help entry for ''quadprog''.
 
- 
-
Problem:
 
-
<pre>
 
-
min 0.5 x0^2 - x0*x1 + x1^2 - 2*x0 - 6*x1,
 
- 
-
subject to
 
-
x0 + x1 <= 2,
 
-
-x0 + 2x1 <= 2,
 
-
2x0 + x1 <= 3,
 
-
x0 >= 0, x1 >= 0.
 
-
</pre>
 
-
MATLAB code:
 
-
<pre>
 
-
clear opts
 
- 
-
c = [-2 -6]; % objective linear term
 
-
objtype = 1; % minimization
 
-
A = sparse([1 1; -1 2; 2 1]); % constraint coefficients
 
-
b = [2; 2; 3]; % constraint right-hand side
 
-
lb = []; % [] means 0 lower bound
 
-
ub = []; % [] means inf upper bound
 
-
contypes = '<<<'; % three <= inequalities
 
-
vtypes = []; % [] means all variables are continuous
 
-
opts.QP.qrow = int32([0 0 1]); % indices of x0, x0, x1 as in (0.5 x0^2 - x0*x1 + x1^2); use int64 if sizeof(int) is 8 for your system
 
-
opts.QP.qcol = int32([0 1 1]); % indices of x0, x1, x1 as in (0.5 x0^2 - x0*x1 + x1^2); use int64 if sizeof(int) is 8 for your system
 
-
opts.QP.qval = [0.5 -1 1]; % coefficients of (0.5 x0^2 - x0*x1 + x1^2)
 
- 
-
opts.IterationLimit = 200;
 
-
opts.FeasibilityTol = 1e-6;
 
-
opts.IntFeasTol = 1e-5;
 
-
opts.OptimalityTol = 1e-6;
 
- 
-
[x,val,exitflag,output,lambda] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
 
- 
-
disp('Solution:');disp(x')
 
-
disp('Optimal obj value:');disp(val)
 
-
disp('Exit flag:');disp(exitflag)
 
-
disp('Optimization info:');disp(output)
 
-
disp('Lagrange multiplers:');disp(lambda')
 
-
</pre>
 
- 
-
Results:
 
-
<pre>
 
-
Solution:
 
-
0.6667 1.3333
 
-
Optimal obj value:
 
-
-8.2222
 
-
Exit flag:
 
-
2
 
-
Optimization info:
 
-
IterCount: 4
 
-
Runtime: 0.0630
 
-
ErrorMsg: []
 
-
Lagrange multiplers:
 
-
-3.1111 -0.4444 0
 
-
</pre>
 
- 
-
=== Example 6. Compressive sensing ===
 
-
See example m-file ''test_gurobi_mex_CS.m''.
 
- 
-
== Feedback ==
 
- 
-
[http://www.convexoptimization.com/wikimization/index.php/Special:Emailuser/Wotao.yin Wotao Yin] would be delighted to hear from you if you find Gurobi Mex useful, or if you have any suggestions, contributions, or bug reports.
 
- 
-
== How to cite ==
 
- 
-
Wotao Yin. ''Gurobi Mex: A MATLAB interface for Gurobi'', URL: http://convexoptimization.com/wikimization/index.php/gurobi_mex, 2009-2011.
 
- 
-
== Download, Installation, and Limitations ==
 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/download_request.html v1.50] ('''Gurobi 4''') latest version C source code and MATLAB examples.
 
- 
-
New features: quadratic programming with no linear constraints. Fixed bugs on handling SOS constraints on 64-bit systems.
 
- 
-
=== History ===
 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.45.zip v1.45] ('''Gurobi 4''') New features: quadratic programming, MIP start vector. Fixed a bug on reporting unsupported options. Dattorro added support for all Gurobi options. Gurobi 4 changed parameter name "LPMethod" to "Method".
 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.35.zip v1.35] '''(Gurobi 2&3)''' New features: support of [http://www.google.com/search?q=special+ordered+set+SOS Special Ordered Sets (SOS)] constraints of types 1 and 2; support all Gurobi parameters and a new option TrapCtrlC; detection of unrecognized options. Fixed minor display issues. Dattorro added support for all Gurobi options.
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.30.zip v1.30] Short release for SOS support.
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.20.zip v1.20] New features: [http://www.caam.rice.edu/~wy1/links/mex_ctrl_c_trick/ Ctrl-C detection], '''Gurobi 3''' support. Improved error and exception handling. Empty array [] is returned if an output argument is not available. Fixed the display interval option.
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.10.zip v1.10] New features: callback, runtime progress output, flexible log file, flexible input types, more options. Part of the code was contributed by ''Tomáš Strnad''.
 
-
Known bug: print an empty line even if options '''DisplayInterval''' and '''Display''' are both set to
 
-
<font face="Times">0</font>. Fix: remove Line 736 of ''gurobi_mex.c'': mexPrintf("\n");
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.05.zip v1.05] Major bug fix: char array of constraint sense has been fixed
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.04.zip v1.04] support writing model to files in various formats such as MPS, REW, LP, ...
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.03.zip v1.03] support log file
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.02.zip v1.02] fixed a memory leak issue
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.01.zip v1.01] update: support output dual solution lambda; allow vartypes to be empty (for all continuous variables).
 
- 
-
[http://www.caam.rice.edu/~wy1/gurobi_mex/gurobi_mex_v1.0.zip v1.00] initial version.
 
- 
-
=== Future Release ===
 
-
Please send your suggested features to [http://www.convexoptimization.com/wikimization/index.php/Special:Emailuser/Wotao.yin Wotao Yin].
 
- 
-
=== Install Gurobi Mex in MATLAB ===
 
- 
-
==== Step 1. Preparation ====
 
-
Refer to [http://www.gurobi.com/doc/40/quickstart/node1.html Gurobi's installation guide]. Make sure that (i) proper environment variables are set, (ii) your copy of Gurobi has a license, and (iii) the license has been successfully validated.
 
- 
-
Make sure that your MATLAB has been set up to use a supported external C compiler such as GCC and MS Visual C++. Run ''mex -setup'' if necessary. Do not use the built-in ''lcc'', which cannot link with Gurobi's library.
 
- 
-
If you use '''Gurobi 2''', uncomment Line 20 of gurobi_mex.c regarding GRB_SUBOPTIMAL.
 
- 
-
'''opts.Method''' in '''Gurobi 4''' corresponds to parameter '''opts.LPMethod''' in '''Gurobi 2''' and '''3'''.
 
- 
-
==== Step 2. Compiling Gurobi Mex ====
 
- 
-
In MATLAB, go to the folder where ''gurobi_mex.c'' is saved and call ''mex'' as follows:
 
- 
-
===== Step 2a. Windows =====
 
- 
-
mex -O -I"<gurobi include path>" "<gurobi_mex.c>" "<gurobi C library file>" "<MATLAB libut.lib>"
 
- 
-
For 64-bit MATLAB, add option "-largeArrayDims".
 
- 
-
Example with '''Gurobi 4''', MSVC2008, MATLAB 2009B, and 32-bit Windows
 
- 
-
mex -O -I"C:\Gurobi400\win32\include" "C:\folder\gurobi_mex.c" "C:\Gurobi400\win32\lib\gurobi40.lib" "C:\Program Files\MATLAB\R2009b\extern\lib\win32\microsoft\libut.lib"
 
- 
-
===== Missing libut.lib? =====
 
-
Ctrl-C detection requires libut.lib. If it is not found under your copy of MATLAB, you can download one for [http://www.caam.rice.edu/~wy1/gurobi_mex/libut_32bit/libut.lib 32-bit Windows] and [http://www.caam.rice.edu/~wy1/gurobi_mex/libut_64bit/libut.lib 64-bit Windows] (courtesy of Imre Polik).
 
- 
-
Alternatively, libut.lib can be manually generated by creating a .def text file including the following five lines
 
-
LIBRARY libut.dll
 
-
EXPORTS
 
-
utIsInterruptPending
 
-
utSetInterruptPending
 
-
[empty line]
 
-
and then calling lib.exe (included in MSVC) like
 
-
"C:\Program Files\Microsoft Visual Studio 9.0\VC\bin\lib" /def:libut.def /out:libut.lib /machine:x86
 
-
where /machine:x86 should be replaced by /machine:x64 for 64-bit Windows.
 
- 
-
===== Step 2b. Linux/Unix =====
 
- 
-
mex -O -I"<gurobi include path>" "<gurobi_mex.c>" -L"<gurobi lib path>" -l<gurobi C library file> -lut
 
- 
-
For 64-bit MATLAB, add option "-largeArrayDims".
 
- 
-
Example with '''Gurobi 3''', GCC, MATLAB 2009B, and 64-bit Linux
 
- 
-
mex -O -I"/opt/gurobi300/linux64/include" "/home/wotao/gurobi mex/gurobi_mex.c" -L"/opt/gurobi300/linux64/lib" -lgurobi30 -lut -largeArrayDims
 
- 
-
==== Tested platforms ====
 
- 
-
* 64-bit Ubuntu Linux 9.10, 64-bit MATLAB, and gcc.
 
-
* 32-bit Windows, 32-bit MATLAB, and gcc (part of free [http://gnumex.sourceforge.net Mingw/GnuMex], alternatively [http://tdm-gcc.tdragon.net TDM-GCC]).
 
-
* 32-bit Windows, 32-bit MATLAB, and MSVC 2008 SP1 (the express Edition is free).
 
-
* 64-bit Windows, 64-bit MATLAB, and MSVC 2008 SP1 (the express Edition is free). Courtesy of Imre Polik.
 
- 
-
For 64-bit MATLAB, Jon Dattorro suggests [http://www.microsoft.com/downloads/details.aspx?FamilyId=A55B6B43-E24F-4EA3-A93E-40C0EC4F68E5&displaylang=en#filelist Microsoft Platform SDK] and a [http://www.mathworks.com/support/solutions/en/data/1-8FJXQE/index.html?solution=1-8FJXQE bug fix] for the linker.
 
- 
-
== FAQs ==
 
-
=== compiling is successful, but gurobi_mex cannot run ===
 
- 
-
'''Solution''': check and correct Gurobi license and environment variables
 
- 
-
Step 1. Check and validate [http://www.gurobi.com/doc/40/quickstart/node2.html Gurobi license]
 
- 
-
Step 2. Check [http://gurobi.com/doc/40/quickstart/node1.html system environment variables for Gurobi]
 
- 
-
Step 3. Verify MATLAB knows the correct system environment variables by running
 
-
>> getenv('GUROBI_HOME')
 
-
>> getenv('GRB_LICENSE_FILE')
 
-
>> getenv('PATH')
 
-
>> getenv('LD_LIBRARY_PATH') % on Unix/Linux/Mac
 
-
You may need to restart MATLAB '''from the terminal''' to get all environment variables loaded to MATLAB.
 
- 
-
=== "int32" or "int64" errors ===
 
- 
-
'''Solution''': use int32 if sizeof(int) is 4 for your system; use int64 if sizeof(int) is 8. To determine sizeof(int), take the following steps
 
- 
-
Step 1. create "check_sizeof_int.c" with the following lines
 
- 
-
#include "mex.h"
 
-
void mexFunction(
 
-
int nlhs, mxArray *plhs[],
 
-
int nrhs, const mxArray *prhs[]
 
-
)
 
-
{
 
-
mexPrintf("Size of int is %d\n", sizeof(int));
 
-
return;
 
-
}
 
- 
-
Step 2. Launch Matlab, run '''mex check_sizeof_int.c''', and then run '''check_sizeof_int'''
 
- 
-
=== MATLAB reports "out of memory" ===
 
- 
-
'''Solution''': run ''clear mex'' after each call to gurobi_mex
 
- 
-
Running out of memory is often the result of memory leaks. However, the interface has been checked numerous times for memory leaks. If there still appears to be a leak, we are not sure if it is with the interface, Gurobi, or MATLAB itself.
 
- 
-
== License ==
 
- 
-
Creative Commons Attribution-Share Alike 3.0 United States License.
 
-
Allow commercial use of this work. Permit others to copy, distribute, display, and perform the work, including for commercial purposes.
 
-
Allow modification, as long as others share alike. Permit others to distribute derivative works only under the same license or one compatible with the one that governs the licensor's work.
 

Revision as of 20:47, 9 June 2011

YALL1-Group is a MATLAB software package for group/joint sparse reconstruction, written by Wei Deng, Wotao Yin and Yin Zhang at Rice University.


Model

(1) Group-sparse basis pursuit model:

                  Minimize     LaTeX: \|x\|_{w,2,1}:=\sum_{i=1}^s w_i\|x_{g_i}\|_2,
  
                  subject to   LaTeX: Ax=b,

where LaTeX: A\in \mathbb{R}^{m\times n}\,(m<n), LaTeX: b\in \mathbb{R}^m, LaTeX: g_i is the index set of the LaTeX: i-th group, and LaTeX: w_i\geq0 is the weight for the LaTeX: i-th group.

(2) Jointly-sparse basis pursuit model:

                  Minimize     LaTeX: \|X\|_{w,2,1}:=\sum_{i=1}^n w_i\|x^i\|_2,
                  subject to   LaTeX: AX=B,

where LaTeX: A\in \mathbb{R}^{m\times n}\,(m<n),\, B\in \mathbb{R}^{m\times l}, LaTeX: x^i is the LaTeX: i-th row of matrix LaTeX: X, and LaTeX: w_i\geq0 is the weight for the LaTeX: i-th row.

Syntax

[x,Out] = YALL1_group(A,b,groups,varargin);

Input Description

Personal tools