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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 \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-19 09:36:12 +0000