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function [x,y,s,z,info,status] = ecos(varargin)
// Solves conic optimization problems with integer and boolean constraints.
//
// Calling Sequence
// x = ecos(c,G,h,dims)
// x = ecos(c,G,h,dims,A,b)
// x = ecos(c,G,h,dims,A,b,options)
// [x,y,s,z,info,status] = ecos( ... )
//
// Parameters
// c : a vector of double, contains coefficients of the variables in the objective.
// G : a matrix of double, represents the linear coefficients in the inequality constraints G⋅x ≤ h with respect to cone K.
// h : a vector of double, represents the linear coefficients in the inequality constraints G⋅x ≤ h with respect to cone K.
// dims : a list containing the number of n-dimensional positive orthant(l),the second order cones(q) and exponential cones(e).
// A : a matrix of double, represents the linear coefficients in the equality constraints A⋅x = b.
// b : a vector of double, represents the linear coefficients in the equality constraints A⋅x = b.
// options : a list containing the parameters to be set.
// x : a vector of double, the primal solution variable of the optimization problem.
// y : a vector of double, the dual variables fo equality constraints of the optimization problem.
// s : a vector of double, the slack for inequality constraints of the optimization problem.
// z : a vector of double, the dula varibale for inequality constraints of the optimization problem.
// info : a struct defining different parameters of the ecos solver. See below for details.
// status : The status returns the solver status after the optimization process. See below for details.
//
// Description
// Search the minimum of a conic constrained mixed integer programming optimization problem specified by :
//
// <latex>
// \begin{eqnarray}
// &\mbox{min}_{x}
// & C^T⋅x \\
// & \text{subject to}& A⋅x = b \\
// & & G⋅x \preceq_K h \\
// & & x_i \in \{0,1\}, i \in \!\, bool_vars\
// & & x_j \in \!\, \mathbb{Z}, i \in \!\, int_vars\\
// \end{eqnarray}
// </latex>
//
// Examples
// // Objective function
// c = [-750 -1000];
// // Constraint inequality matrix LHS
// G = [
// 1 1;
// 1 2;
// 4 3;
// ];
// // Constraint inequality matrix RHS
// h = [10 15 25]';
// // Constraint equality matrix LHS
// A = [
// 0.5 1
// ];
// // Constraint equality matrix RHS
// b=[7.5];
// // Dimension of positive orthant
// l = [3];
// q = [];
// e = [];
// dims=list("l",l,"q",q,"e",e)
// //Calling ecos
// [x,y,s,z,info,status] =ecos(c,G,h,dims,A,b);
// Examples
//
// // Objective function
// c = [0 0 0 0 1];
// //Constraint inequality matrix LHS
// G = [
// 0.4167578 0.0562668 0. 0. 0.
// 2.1361961 -1.6402708 0. 0. 0.
// 1.7934356 0.8417474 0. 0. 0.
// 0. 0. 0.4167578 0.0562668 0.
// 0. 0. 2.1361961 -1.6402708 0.
// 0. 0. 1.7934356 0.8417474 0.
// 0. 0. 0. 0. -1.
// -1. 0. 0. 0. 0.
// 0. -1. 0. 0. 0.
// 0. 0. -1. 0. 0.
// 0. 0. 0. -1. 0.
// ];
// //Constraint inequality matrix RHS
// h = [0 0 0 0 0 0 0 0 0 0 0]';
// // Dimension of positive orthant
// l = [6];
// q = [5];
// e = [0]
// dims=list("l",l,"q",q,"e",e)
// [x,y,s,z,info,status] =ecos(c,G,h,dims);
// Author
// Georgey John
function [A1,b1,s0]=linconcheck(A,b,inputs_name)
//Function to check the linear inputs A,b and Aeq,beq
if(size(b,2)>1) then
errmsg = msprintf(gettext("%s: Expected Column vector of size (Number of constraints) for %s"), "ecos",inputs_name(2));
error(errmsg);
end
s0=size(A);
//To check for correct size of A
if(s0(2)==0) then
if(size(b,2)~=0) then
errmsg = msprintf(gettext("%s: As Linear Inequality Constraint coefficient Matrix %s is empty, %s should also be empty"), "ecos",inputs_name(1),inputs_name(2));
error(errmsg);
end
else
if((size(b,1)~=1) & (size(b,2)~=1)) then
errmsg = msprintf(gettext("%s: Expected Non empty Row/Column Vector for %s for your Inputs "), "ecos",inputs_name(2));
error(errmsg);
elseif(size(b,1)~=s0(1) & size(b,2)==1) then
errmsg = msprintf(gettext("%s: Expected Column Vector (number of linear inequality constraints X 1) for %s"), "ecos",inputs_name(2));
error(errmsg);
// elseif(size(b,1)==1 & size(b,2)~=s0(1)) then
// errmsg = msprintf(gettext("%s: Expected Row Vector (1 X number of linear inequality constraints) for %s"), "ecos",inputs_name(2));
// error(errmsg);
end
end
b1=b;
//To check for corrcet size of A
if(size(A,1)~=size(b,1) & size(A,2)~=0) then
errmsg = msprintf(gettext("%s: Expected Matrix of size (No of linear inequality constraints X No of Variables) or an Empty Matrix for Linear Inequality Constraint coefficient Matrix %s"), "ecos",inputs_name(1));
error(errmsg);
end
A1=A;
endfunction
[lhs ,rhs]=argn()
if ( rhs<4 | rhs>9 ) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while it should be 4,6,7,8 or 9"), "ecos", rhs);
error(errmsg);
end
if (rhs==5) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while it should be 4,6,8,10 or 11"), "ecos", rhs);
error(errmsg);
end
c = varargin(1);
G = varargin(2);
h = varargin(3);
dims = varargin(4);
A=[];Apr=[];Ajc=[];Air=[];
b=[];
param=list();
m=0,n=0,p=0;
if (rhs>4 & rhs<7) then
A = varargin(5);
b = varargin(6);
else
A=[];
b=[];
end
if (rhs ==7) then
param = varargin(7);
end
Checktype("ecos", c, "c", 1, "constant");
// Error check for objective matrix(c)
if (size(c,1)~=1) then
errmsg = msprintf(gettext("%s: c should be a row vector"), "ecos");
error(errmsg);
elseif (size(c,1)==0) then
errmsg = msprintf(gettext("%s: c cannot be empty"), "ecos");
error(errmsg);
end
s=size(c,2);
Checktype("ecos", G, "G", 2, "constant");
Checktype("ecos", h, "h", 3, "constant");
[m,n]=size(G);
// Error check and converting inequaity matrix(G) to CCS format required by ecos
if (n~=size(c,2)) then
errmsg = msprintf(gettext("%s: Number of columns of G and c do not match"), "ecos");
error(errmsg);
end
[G,h,s1]=linconcheck(G,h,["G","h"]);
[Gjc,Gir,Gpr] = sp2adj(sparse(G));
// Extracting values and Error checks for dims
Checktype("ecos", dims, "dims", 4, "list");
if (isempty(dims) | modulo(size(dims),2)) then
errmsg = msprintf(gettext("%s: dims cannot be empty and should be list of even size"), "ecos");
error(errmsg);
end
for i = 1:(size(dims))/2
select convstr(dims(2*i-1),'l')
case "l" then
Checktype("ecos", dims(2*i), "l", 4, "constant");
if (isempty(dims(2*i))) then
l=0;
elseif (dims(2*i)<0 | modulo(dims(2*i),1)) then
errmsg = msprintf(gettext("%s: l in dims should be a positive integer"), "ecos");
error(errmsg);
else
l=dims(2*i);
// if (prod(size(l))>1)) then
// errmsg = msprintf(gettext("%s: l in dims should be a positive integer"), "ecos");
// error(errmsg);
// end
end
case "q" then
Checktype("ecos", dims(2*i), "q", 4, "constant");
if (isempty(dims(2*i))) then
q=[];
elseif (dims(2*i)<0 | modulo(dims(2*i),1)) then
errmsg = msprintf(gettext("%s: q in dims should be a positive vector"), "ecos");
error(errmsg);
else
q=dims(2*i);
end
case "e" then
Checktype("ecos", dims(2*i), "e", 4, "constant");
if (isempty(dims(2*i))) then
e=0;
elseif (dims(2*i)<0 | modulo(dims(2*i),1)) then
errmsg = msprintf(gettext("%s: e in dims should be a positive integer"), "ecos");
error(errmsg);
else
e=dims(2*i);
// if (prod(size(e))>1)) then
// errmsg = msprintf(gettext("%s: e in dims should be a positive integer"), "ecos");
// error(errmsg);
// end
end
else
errmsg = msprintf(gettext("%s: Unrecognized parameter name %s."), "ecos", dims(2*i-1));
error(errmsg);
end
end
// Error check and converting equaity matrix(A) to CCS format required by ecos
if ((size(A,1)*size(b,1)==0) & (size(A,1)+size(b,1)~=0)) then
errmsg = msprintf(gettext("%s: One of %s and %s is an empty matrix"), "ecos","A","b");
error(errmsg);
end
if (size(A,1)~=0) then
Checktype("ecos", A, "A", 5, "constant");
Checktype("ecos", b, "b", 6, "constant");
[A,b,s2]=linconcheck(A,b,["A","b"]);
[Ajc,Air,Apr] = sp2adj(sparse(A));
[m2,p]= size(A);
if (n~=p) then
errmsg = msprintf(gettext("%s: Number of columns of G and A do not match"), "ecos");
error(errmsg);
end
if (p~=size(c,2)) then
errmsg = msprintf(gettext("%s: Number of columns of A and c do not match"), "ecos");
error(errmsg);
end
end
if (size(G,1)==0 & (size(h,1)==0)) then
if (size(A,1)==0 & (size(b,1)==0)) then
errmsg = msprintf(gettext("%s: At most one of the pair (G, h) or (A, b) is allowed to be absent"), "ecos");
error(errmsg);
end
end
// Extracting values and Error checks for options(param)
Checktype("ecos", param, "param", 1, "list");
if (modulo(size(param),2)) then
errmsg = msprintf(gettext("%s: Size of Options (list) should be even"), "ecos");
error(errmsg);
end
option = list("maxiter", [100], "feastol", [1e-8],"reltol",[1e-8],"abstol",[1e-8],"feastol_inacc",[1e-4],"abstol_inacc",[5e-5],"reltol_inacc",[5e-5],"verbose",[0],"mi_max_iters",[1000],"mi_int_tol",[1e-4],"mi_abs_eps",[1e-6],"mi_rel_eps",[1e-6]);
for i = 1:(size(param))/2
select convstr(param(2*i-1),'l')
case "maxit" then
if (type(option(2*i))~=1 | modulo(option(2*i),1)) then
errmsg = msprintf(gettext("%s: Value for Maximum Iteration should be a Constant integer"), "ecos");
error(errmsg);
else
option(2) = param(2*i);
end
case "feastol" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for tolerance should be a Constant"), "ecos");
error(errmsg);
else
option(4) = param(2*i);
end
case "reltol" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for relative tolerance should be a Constant"), "ecos");
error(errmsg);
else
option(6) = param(2*i);
end
case "abstol" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for absolute tolerance should be a Constant"), "ecos");
error(errmsg);
else
option(8) = param(2*i);
end
case "feastol_inacc" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for tolerance with reduced precision should be a Constant"), "ecos");
error(errmsg);
else
option(10) = param(2*i);
end
case "reltol_inacc" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for relative tolerance with reduced precision should be a Constant"), "ecos");
error(errmsg);
else
option(12) = param(2*i);
end
case "abstol_inacc" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for absolute tolerance with reduced precision should be a Constant"), "ecos");
error(errmsg);
else
option(14) = param(2*i);
end
case "verbose" then
if (type(option(2*i))~=1 | modulo(option(2*i),1)) then
errmsg = msprintf(gettext("%s: Value for verbose level should be a Constant integer"), "ecos");
error(errmsg);
else
option(16) = param(2*i);
end
case "mi_max_iters" then
if (type(option(2*i))~=1 | modulo(option(2*i),1)) then
errmsg = msprintf(gettext("%s: Value for maximum branch and bound iterations should be a Constant integer"), "ecos");
error(errmsg);
else
option(18) = param(2*i);
end
case "mi_int_tol" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for integer tolerance should be a Constant"), "ecos");
error(errmsg);
else
option(20) = param(2*i);
end
case "mi_abs_eps" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for absolute tolerance between upper and lower bounds should be a Constant"), "ecos");
error(errmsg);
else
option(22) = param(2*i);
end
case "mi_rel_eps" then
if (type(option(2*i))~=1) then
errmsg = msprintf(gettext("%s: Value for relative tolerance between upper and lower bounds should be a Constant"), "ecos");
error(errmsg);
else
option(24) = param(2*i);
end
else
errmsg = msprintf(gettext("%s: Unrecognized parameter name %s."), "ecos", param(2*i-1));
error(errmsg);
end
end
// number of second order cones is size of q
ncones = size(q,2);
//Converting form 1-based(Scilab) indexing to 0-based indexing(C)
Gjc=Gjc-1;
Gir=Gir-1;
if (p ~=0)
Ajc=Ajc-1;
Air=Air-1;
end
// Calling ecos
[x,y,info1,s,z]=solveecos(c,Gpr,int32(Gjc),int32(Gir),h,Apr,int32(Ajc),int32(Air),b,l,int32(q),e,option,m,n,p,ncones)
// Assigning output parameters
info=struct();
info.setup_time=info1(1);
info.solve_time = info1(2);
info.primal_objective_cost =info1(3);
info.dual_objective_cost =info1(4);
info.Normalized_primal_residual = info1(5);
info.Normalized_dual_residual = info1(6);
info.primal_infeasibile = info1(7);
info.dual_infeasibile = info1(8);
info.primal_infeasibility_measure = info1(9);
info.dual_infeasibility_measure = info1(10);
info.Complementarity_gap = info1(11);
info.Normalized_complementarity_gap = info1(12);
info.Iterations = info1(13);
info.exitflag = info1(14);
// Status
select info.exitflag
case 0 then
status='Optimal solution found';
case 1 then
status='Certificate of primal infeasibility found';
case 2 then
status='Certificate of dual infeasibility found';
case 10 then
status='Optimal solution found subject to reduced tolerances';
case 11 then
status='Certificate of primal infeasibility found subject to reduced tolerances';
case 12 then
status='Certificate of dual infeasibility found subject to reduced tolerances';
case -1 then
status='Maximum number of iterations reached';
case -2 then
status='Numerical problems (unreliable search direction)';
case -3 then
status='Numerical problems (slacks or multipliers outside cone)';
case -4 then
status='Interrupted by signal or CTRL-C';
case -7 then
status='Unknown problem in solver';
case -8 then
status='ecos setup error';
else
status='Unknown problem in toolbox,contact toolbox authors';
end
disp(status);
endfunction
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