Home > matpower6.0 > qps_glpk.m

qps_glpk

PURPOSE ^

QPS_GLPK Linear Program Solver based on GLPK - GNU Linear Programming Kit.

SYNOPSIS ^

function [x, f, eflag, output, lambda] = qps_glpk(H, c, A, l, u, xmin, xmax, x0, opt)

DESCRIPTION ^

QPS_GLPK  Linear Program Solver based on GLPK - GNU Linear Programming Kit.
   [X, F, EXITFLAG, OUTPUT, LAMBDA] = ...
       QPS_GLPK(H, C, A, L, U, XMIN, XMAX, X0, OPT)
   A wrapper function providing a MATPOWER standardized interface for using
   GLKP to solve the following LP (linear programming) problem:

       min C'*X
        X

   subject to

       L <= A*X <= U       (linear constraints)
       XMIN <= X <= XMAX   (variable bounds)

   Inputs (all optional except H, C, A and L):
       H : dummy matrix (possibly sparse) of quadratic cost coefficients
           for QP problems, which GLPK does not handle
       C : vector of linear cost coefficients
       A, L, U : define the optional linear constraints. Default
           values for the elements of L and U are -Inf and Inf,
           respectively.
       XMIN, XMAX : optional lower and upper bounds on the
           X variables, defaults are -Inf and Inf, respectively.
       X0 : optional starting value of optimization vector X (NOT USED)
       OPT : optional options structure with the following fields,
           all of which are also optional (default values shown in
           parentheses)
           verbose (0) - controls level of progress output displayed
               0 = no progress output
               1 = some progress output
               2 = verbose progress output
           glpk_opt - options struct for GLPK, value in
               verbose overrides these options
       PROBLEM : The inputs can alternatively be supplied in a single
           PROBLEM struct with fields corresponding to the input arguments
           described above: H, c, A, l, u, xmin, xmax, x0, opt

   Outputs:
       X : solution vector
       F : final objective function value
       EXITFLAG : exit flag, 1 - optimal, <= 0 - infeasible, unbounded or other
       OUTPUT : struct with errnum and status fields from GLPK output args
       LAMBDA : struct containing the Langrange and Kuhn-Tucker
           multipliers on the constraints, with fields:
           mu_l - lower (left-hand) limit on linear constraints
           mu_u - upper (right-hand) limit on linear constraints
           lower - lower bound on optimization variables
           upper - upper bound on optimization variables

   Note the calling syntax is almost identical to that of GLPK. The main
   difference is that the linear constraints are specified with A, L, U
   instead of A, B, Aeq, Beq.

   Calling syntax options:
       [x, f, exitflag, output, lambda] = ...
           qps_glpk(H, c, A, l, u, xmin, xmax, x0, opt)

       x = qps_glpk(H, c, A, l, u)
       x = qps_glpk(H, c, A, l, u, xmin, xmax)
       x = qps_glpk(H, c, A, l, u, xmin, xmax, x0)
       x = qps_glpk(H, c, A, l, u, xmin, xmax, x0, opt)
       x = qps_glpk(problem), where problem is a struct with fields:
                       H, c, A, l, u, xmin, xmax, x0, opt
                       all fields except 'c', 'A' and 'l' or 'u' are optional
       x = qps_glpk(...)
       [x, f] = qps_glpk(...)
       [x, f, exitflag] = qps_glpk(...)
       [x, f, exitflag, output] = qps_glpk(...)
       [x, f, exitflag, output, lambda] = qps_glpk(...)


   Example: (problem from from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm)
       H = [   1003.1  4.3     6.3     5.9;
               4.3     2.2     2.1     3.9;
               6.3     2.1     3.5     4.8;
               5.9     3.9     4.8     10  ];
       c = zeros(4,1);
       A = [   1       1       1       1;
               0.17    0.11    0.10    0.18    ];
       l = [1; 0.10];
       u = [1; Inf];
       xmin = zeros(4,1);
       x0 = [1; 0; 0; 1];
       opt = struct('verbose', 2);
       [x, f, s, out, lambda] = qps_glpk(H, c, A, l, u, xmin, [], x0, opt);

   See also GLPK.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [x, f, eflag, output, lambda] = qps_glpk(H, c, A, l, u, xmin, xmax, x0, opt)
0002 %QPS_GLPK  Linear Program Solver based on GLPK - GNU Linear Programming Kit.
0003 %   [X, F, EXITFLAG, OUTPUT, LAMBDA] = ...
0004 %       QPS_GLPK(H, C, A, L, U, XMIN, XMAX, X0, OPT)
0005 %   A wrapper function providing a MATPOWER standardized interface for using
0006 %   GLKP to solve the following LP (linear programming) problem:
0007 %
0008 %       min C'*X
0009 %        X
0010 %
0011 %   subject to
0012 %
0013 %       L <= A*X <= U       (linear constraints)
0014 %       XMIN <= X <= XMAX   (variable bounds)
0015 %
0016 %   Inputs (all optional except H, C, A and L):
0017 %       H : dummy matrix (possibly sparse) of quadratic cost coefficients
0018 %           for QP problems, which GLPK does not handle
0019 %       C : vector of linear cost coefficients
0020 %       A, L, U : define the optional linear constraints. Default
0021 %           values for the elements of L and U are -Inf and Inf,
0022 %           respectively.
0023 %       XMIN, XMAX : optional lower and upper bounds on the
0024 %           X variables, defaults are -Inf and Inf, respectively.
0025 %       X0 : optional starting value of optimization vector X (NOT USED)
0026 %       OPT : optional options structure with the following fields,
0027 %           all of which are also optional (default values shown in
0028 %           parentheses)
0029 %           verbose (0) - controls level of progress output displayed
0030 %               0 = no progress output
0031 %               1 = some progress output
0032 %               2 = verbose progress output
0033 %           glpk_opt - options struct for GLPK, value in
0034 %               verbose overrides these options
0035 %       PROBLEM : The inputs can alternatively be supplied in a single
0036 %           PROBLEM struct with fields corresponding to the input arguments
0037 %           described above: H, c, A, l, u, xmin, xmax, x0, opt
0038 %
0039 %   Outputs:
0040 %       X : solution vector
0041 %       F : final objective function value
0042 %       EXITFLAG : exit flag, 1 - optimal, <= 0 - infeasible, unbounded or other
0043 %       OUTPUT : struct with errnum and status fields from GLPK output args
0044 %       LAMBDA : struct containing the Langrange and Kuhn-Tucker
0045 %           multipliers on the constraints, with fields:
0046 %           mu_l - lower (left-hand) limit on linear constraints
0047 %           mu_u - upper (right-hand) limit on linear constraints
0048 %           lower - lower bound on optimization variables
0049 %           upper - upper bound on optimization variables
0050 %
0051 %   Note the calling syntax is almost identical to that of GLPK. The main
0052 %   difference is that the linear constraints are specified with A, L, U
0053 %   instead of A, B, Aeq, Beq.
0054 %
0055 %   Calling syntax options:
0056 %       [x, f, exitflag, output, lambda] = ...
0057 %           qps_glpk(H, c, A, l, u, xmin, xmax, x0, opt)
0058 %
0059 %       x = qps_glpk(H, c, A, l, u)
0060 %       x = qps_glpk(H, c, A, l, u, xmin, xmax)
0061 %       x = qps_glpk(H, c, A, l, u, xmin, xmax, x0)
0062 %       x = qps_glpk(H, c, A, l, u, xmin, xmax, x0, opt)
0063 %       x = qps_glpk(problem), where problem is a struct with fields:
0064 %                       H, c, A, l, u, xmin, xmax, x0, opt
0065 %                       all fields except 'c', 'A' and 'l' or 'u' are optional
0066 %       x = qps_glpk(...)
0067 %       [x, f] = qps_glpk(...)
0068 %       [x, f, exitflag] = qps_glpk(...)
0069 %       [x, f, exitflag, output] = qps_glpk(...)
0070 %       [x, f, exitflag, output, lambda] = qps_glpk(...)
0071 %
0072 %
0073 %   Example: (problem from from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm)
0074 %       H = [   1003.1  4.3     6.3     5.9;
0075 %               4.3     2.2     2.1     3.9;
0076 %               6.3     2.1     3.5     4.8;
0077 %               5.9     3.9     4.8     10  ];
0078 %       c = zeros(4,1);
0079 %       A = [   1       1       1       1;
0080 %               0.17    0.11    0.10    0.18    ];
0081 %       l = [1; 0.10];
0082 %       u = [1; Inf];
0083 %       xmin = zeros(4,1);
0084 %       x0 = [1; 0; 0; 1];
0085 %       opt = struct('verbose', 2);
0086 %       [x, f, s, out, lambda] = qps_glpk(H, c, A, l, u, xmin, [], x0, opt);
0087 %
0088 %   See also GLPK.
0089 
0090 %   MATPOWER
0091 %   Copyright (c) 2010-2016, Power Systems Engineering Research Center (PSERC)
0092 %   by Ray Zimmerman, PSERC Cornell
0093 %
0094 %   This file is part of MATPOWER.
0095 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0096 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0097 
0098 %% check for Optimization Toolbox
0099 % if ~have_fcn('quadprog')
0100 %     error('qps_glpk: requires the MEX interface to GLPK');
0101 % end
0102 
0103 %%----- input argument handling  -----
0104 %% gather inputs
0105 if nargin == 1 && isstruct(H)       %% problem struct
0106     p = H;
0107     if isfield(p, 'opt'),   opt = p.opt;    else,   opt = [];   end
0108     if isfield(p, 'x0'),    x0 = p.x0;      else,   x0 = [];    end
0109     if isfield(p, 'xmax'),  xmax = p.xmax;  else,   xmax = [];  end
0110     if isfield(p, 'xmin'),  xmin = p.xmin;  else,   xmin = [];  end
0111     if isfield(p, 'u'),     u = p.u;        else,   u = [];     end
0112     if isfield(p, 'l'),     l = p.l;        else,   l = [];     end
0113     if isfield(p, 'A'),     A = p.A;        else,   A = [];     end
0114     if isfield(p, 'c'),     c = p.c;        else,   c = [];     end
0115     if isfield(p, 'H'),     H = p.H;        else,   H = [];     end
0116 else                                %% individual args
0117     if nargin < 9
0118         opt = [];
0119         if nargin < 8
0120             x0 = [];
0121             if nargin < 7
0122                 xmax = [];
0123                 if nargin < 6
0124                     xmin = [];
0125                 end
0126             end
0127         end
0128     end
0129 end
0130 
0131 %% define nx, set default values for missing optional inputs
0132 if isempty(H) || ~any(any(H))
0133     if isempty(A) && isempty(xmin) && isempty(xmax)
0134         error('qps_glpk: LP problem must include constraints or variable bounds');
0135     else
0136         if ~isempty(A)
0137             nx = size(A, 2);
0138         elseif ~isempty(xmin)
0139             nx = length(xmin);
0140         else    % if ~isempty(xmax)
0141             nx = length(xmax);
0142         end
0143     end
0144 else
0145     error('qps_glpk: GLPK handles only LP problems, not QP problems');
0146     nx = size(H, 1);
0147 end
0148 if isempty(c)
0149     c = zeros(nx, 1);
0150 end
0151 if isempty(A) || (~isempty(A) && (isempty(l) || all(l == -Inf)) && ...
0152                                  (isempty(u) || all(u == Inf)))
0153     A = sparse(0,nx);           %% no limits => no linear constraints
0154 end
0155 nA = size(A, 1);                %% number of original linear constraints
0156 if isempty(u)                   %% By default, linear inequalities are ...
0157     u = Inf(nA, 1);             %% ... unbounded above and ...
0158 end
0159 if isempty(l)
0160     l = -Inf(nA, 1);            %% ... unbounded below.
0161 end
0162 if isempty(xmin)                %% By default, optimization variables are ...
0163     xmin = -Inf(nx, 1);         %% ... unbounded below and ...
0164 end
0165 if isempty(xmax)
0166     xmax = Inf(nx, 1);          %% ... unbounded above.
0167 end
0168 if isempty(x0)
0169     x0 = zeros(nx, 1);
0170 end
0171 
0172 %% default options
0173 if ~isempty(opt) && isfield(opt, 'verbose') && ~isempty(opt.verbose)
0174     verbose = opt.verbose;
0175 else
0176     verbose = 0;
0177 end
0178 
0179 %% split up linear constraints
0180 ieq = find( abs(u-l) <= eps );          %% equality
0181 igt = find( u >=  1e10 & l > -1e10 );   %% greater than, unbounded above
0182 ilt = find( l <= -1e10 & u <  1e10 );   %% less than, unbounded below
0183 ibx = find( (abs(u-l) > eps) & (u < 1e10) & (l > -1e10) );
0184 AA = [ A(ieq, :); A(ilt, :); -A(igt, :); A(ibx, :); -A(ibx, :) ];
0185 bb = [ u(ieq);    u(ilt);    -l(igt);    u(ibx);    -l(ibx)];
0186 
0187 %% grab some dimensions
0188 nlt = length(ilt);      %% number of upper bounded linear inequalities
0189 ngt = length(igt);      %% number of lower bounded linear inequalities
0190 nbx = length(ibx);      %% number of doubly bounded linear inequalities
0191 neq = length(ieq);      %% number of equalities
0192 nie = nlt+ngt+2*nbx;    %% number of inequalities
0193 
0194 ctype = [repmat('S', neq, 1); repmat('U', nlt+ngt+2*nbx, 1)];
0195 vtype = repmat('C', nx, 1);
0196 
0197 %% set options struct for GLPK
0198 if ~isempty(opt) && isfield(opt, 'glpk_opt') && ~isempty(opt.glpk_opt)
0199     glpk_opt = glpk_options(opt.glpk_opt);
0200 else
0201     glpk_opt = glpk_options;
0202 end
0203 glpk_opt.msglev = verbose;
0204 
0205 %% call the solver
0206 [x, f, errnum, extra] = ...
0207     glpk(c, AA, bb, xmin, xmax, ctype, vtype, 1, glpk_opt);
0208 
0209 %% set exit flag
0210 if isfield(extra, 'status')             %% status found in extra.status
0211     output.errnum = errnum;
0212     output.status = extra.status;
0213     eflag = -errnum;
0214     if eflag == 0 && extra.status == 5
0215         eflag = 1;
0216     end
0217 else                                    %% status found in errnum
0218     output.errnum = [];
0219     output.status = errnum;
0220     if have_fcn('octave')
0221         if errnum == 180 || errnum == 151 || errnum == 171
0222             eflag = 1;
0223         else
0224             eflag = 0;
0225         end
0226     else
0227         if errnum == 5
0228             eflag = 1;
0229         else
0230             eflag = 0;
0231         end
0232     end
0233 end
0234 
0235 %% repackage lambdas
0236 if isempty(extra) || ~isfield(extra, 'lambda') || isempty(extra.lambda)
0237     lambda = struct( ...
0238         'mu_l', zeros(nA, 1), ...
0239         'mu_u', zeros(nA, 1), ...
0240         'lower', zeros(nx, 1), ...
0241         'upper', zeros(nx, 1) ...
0242     );
0243 else
0244     lam.eqlin = extra.lambda(1:neq);
0245     lam.ineqlin = extra.lambda(neq+(1:nie));
0246     lam.lower = extra.redcosts;
0247     lam.upper = -extra.redcosts;
0248     lam.lower(lam.lower < 0) = 0;
0249     lam.upper(lam.upper < 0) = 0;
0250     kl = find(lam.eqlin > 0);   %% lower bound binding
0251     ku = find(lam.eqlin < 0);   %% upper bound binding
0252 
0253     mu_l = zeros(nA, 1);
0254     mu_l(ieq(kl)) = lam.eqlin(kl);
0255     mu_l(igt) = -lam.ineqlin(nlt+(1:ngt));
0256     mu_l(ibx) = -lam.ineqlin(nlt+ngt+nbx+(1:nbx));
0257 
0258     mu_u = zeros(nA, 1);
0259     mu_u(ieq(ku)) = -lam.eqlin(ku);
0260     mu_u(ilt) = -lam.ineqlin(1:nlt);
0261     mu_u(ibx) = -lam.ineqlin(nlt+ngt+(1:nbx));
0262 
0263     lambda = struct( ...
0264         'mu_l', mu_l, ...
0265         'mu_u', mu_u, ...
0266         'lower', lam.lower(1:nx), ...
0267         'upper', lam.upper(1:nx) ...
0268     );
0269 end

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