0001 function t_miqps_matpower(quiet)
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012
0013
0014 if nargin < 1
0015 quiet = 0;
0016 end
0017
0018 algs = {'CPLEX', 'MOSEK', 'GUROBI', 'GLPK', 'OT'};
0019 names = {'CPLEX', 'MOSEK', 'Gurobi', 'glpk', 'intlin/lin/quadprog'};
0020 check = {'cplex', 'mosek', 'gurobi', 'glpk', 'intlinprog'};
0021 does_qp = [1 1 1 0 0];
0022
0023 n = 48;
0024 nqp = 28;
0025 nmiqp = 6;
0026 t_begin(n*length(algs), quiet);
0027
0028 for k = 1:length(algs)
0029 if ~isempty(check{k}) && ~have_fcn(check{k})
0030 t_skip(n, sprintf('%s not installed', names{k}));
0031 else
0032 opt = struct('verbose', 0, 'alg', algs{k});
0033 if strcmp(names{k}, 'CPLEX')
0034
0035 alg = 2;
0036 mpopt = mpoption('cplex.lpmethod', alg, 'cplex.qpmethod', min([4 alg]));
0037 opt.cplex_opt = cplex_options([], mpopt);
0038 end
0039 if strcmp(names{k}, 'MOSEK')
0040 mpopt = mpoption;
0041
0042
0043
0044 mpopt = mpoption(mpopt, 'mosek.gap_tol', 1e-10);
0045 opt.mosek_opt = mosek_options([], mpopt);
0046 end
0047
0048 t = sprintf('%s - 3-d LP : ', names{k});
0049
0050 c = [-5; -4; -6];
0051 A = [1 -1 1;
0052 -3 -2 -4;
0053 3 2 0];
0054 l = [-Inf; -42; -Inf];
0055 u = [20; Inf; 30];
0056 xmin = [0; 0; 0];
0057 x0 = [];
0058 [x, f, s, out, lam] = miqps_matpower([], c, A, l, u, xmin, [], [], [], opt);
0059 t_is(s, 1, 12, [t 'success']);
0060 t_is(x, [0; 15; 3], 6, [t 'x']);
0061 t_is(f, -78, 6, [t 'f']);
0062 t_is(lam.mu_l, [0;1.5;0], 9, [t 'lam.mu_l']);
0063 t_is(lam.mu_u, [0;0;0.5], 9, [t 'lam.mu_u']);
0064 t_is(lam.lower, [1;0;0], 9, [t 'lam.lower']);
0065 t_is(lam.upper, zeros(size(x)), 9, [t 'lam.upper']);
0066
0067 if does_qp(k)
0068 t = sprintf('%s - unconstrained 3-d quadratic : ', names{k});
0069
0070 H = [5 -2 -1; -2 4 3; -1 3 5];
0071 c = [2; -35; -47];
0072 x0 = [0; 0; 0];
0073 [x, f, s, out, lam] = miqps_matpower(H, c, [], [], [], [], [], [], [], opt);
0074 t_is(s, 1, 12, [t 'success']);
0075 t_is(x, [3; 5; 7], 8, [t 'x']);
0076 t_is(f, -249, 13, [t 'f']);
0077 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0078 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0079 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0080 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0081
0082 t = sprintf('%s - constrained 2-d QP : ', names{k});
0083
0084 H = [ 1 -1;
0085 -1 2 ];
0086 c = [-2; -6];
0087 A = [ 1 1;
0088 -1 2;
0089 2 1 ];
0090 l = [];
0091 u = [2; 2; 3];
0092 xmin = [0; 0];
0093 x0 = [];
0094 [x, f, s, out, lam] = miqps_matpower(H, c, A, l, u, xmin, [], x0, [], opt);
0095 t_is(s, 1, 12, [t 'success']);
0096 t_is(x, [2; 4]/3, 7, [t 'x']);
0097 t_is(f, -74/9, 6, [t 'f']);
0098 t_is(lam.mu_l, [0;0;0], 13, [t 'lam.mu_l']);
0099 t_is(lam.mu_u, [28;4;0]/9, 7, [t 'lam.mu_u']);
0100 t_is(lam.lower, zeros(size(x)), 7, [t 'lam.lower']);
0101 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0102
0103 t = sprintf('%s - constrained 4-d QP : ', names{k});
0104
0105 H = [ 1003.1 4.3 6.3 5.9;
0106 4.3 2.2 2.1 3.9;
0107 6.3 2.1 3.5 4.8;
0108 5.9 3.9 4.8 10 ];
0109 c = zeros(4,1);
0110 A = [ 1 1 1 1;
0111 0.17 0.11 0.10 0.18 ];
0112 l = [1; 0.10];
0113 u = [1; Inf];
0114 xmin = zeros(4,1);
0115 x0 = [1; 0; 0; 1];
0116 [x, f, s, out, lam] = miqps_matpower(H, c, A, l, u, xmin, [], x0, [], opt);
0117 t_is(s, 1, 12, [t 'success']);
0118 t_is(x, [0; 2.8; 0.2; 0]/3, 5, [t 'x']);
0119 t_is(f, 3.29/3, 6, [t 'f']);
0120 t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
0121 t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
0122 t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
0123 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0124
0125 t = sprintf('%s - (struct) constrained 4-d QP : ', names{k});
0126 p = struct('H', H, 'A', A, 'l', l, 'u', u, 'xmin', xmin, 'x0', x0, 'opt', opt);
0127 [x, f, s, out, lam] = miqps_matpower(p);
0128 t_is(s, 1, 12, [t 'success']);
0129 t_is(x, [0; 2.8; 0.2; 0]/3, 5, [t 'x']);
0130 t_is(f, 3.29/3, 6, [t 'f']);
0131 t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
0132 t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
0133 t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
0134 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0135 else
0136 t_skip(nqp, sprintf('%s does not handle QP problems', names{k}));
0137 end
0138
0139 t = sprintf('%s - infeasible LP : ', names{k});
0140 p = struct('A', sparse([1 1]), 'c', [1;1], 'u', -1, 'xmin', [0;0], 'opt', opt);
0141 [x, f, s, out, lam] = miqps_matpower(p);
0142 t_ok(s <= 0, [t 'no success']);
0143
0144
0145 t = sprintf('%s - 2-d MILP : ', names{k});
0146
0147 c = [-2; -3];
0148 A = sparse([195 273; 4 40]);
0149 u = [1365; 140];
0150 xmax = [4; Inf];
0151 vtype = 'I';
0152 p = struct('c', c, 'A', A, 'u', u, 'xmax', xmax, 'vtype', vtype, 'opt', opt);
0153 [x, f, s, out, lam] = miqps_matpower(p);
0154 t_is(s, 1, 12, [t 'success']);
0155 t_is(x, [4; 2], 12, [t 'x']);
0156 t_is(lam.mu_l, [0; 0], 12, [t 'lam.mu_l']);
0157 t_is(lam.mu_u, [0; 0], 12, [t 'lam.mu_u']);
0158 t_is(lam.lower, [0; 0], 12, [t 'lam.lower']);
0159 t_is(lam.upper, [2; 3], 12, [t 'lam.upper']);
0160
0161 if does_qp(k)
0162 t = sprintf('%s - 4-d MIQP : ', names{k});
0163
0164 H = sparse([ 33 6 0 0;
0165 6 22 11.5 0;
0166 0 11.5 11 0;
0167 0 0 0 0]);
0168 c = [-1 -2 -3 -1]';
0169 Aineq = [-1 1 1 10;
0170 1 -3 1 0];
0171 bineq = [20 30]';
0172 Aeq = [0 1 0 -3.5];
0173 beq = 0;
0174 xmin = [ 0; 0; 0; 2];
0175 xmax = [40; Inf; Inf; 3];
0176 A = sparse([Aeq; Aineq]);
0177 l = [beq; -Inf; -Inf];
0178 u = [beq; bineq];
0179 vtype = 'CCCI';
0180 p = struct('H', H, 'c', c, 'A', A, 'l', l, 'u', u, ...
0181 'xmin', xmin, 'xmax', xmax, 'vtype', vtype, 'opt', opt);
0182 [x, f, s, out, lam] = miqps_matpower(p);
0183 t_is(s, 1, 12, [t 'success']);
0184 t_is(x, [7; 7; 0; 2], 7, [t 'x']);
0185 t_is(lam.mu_l, [466; 0; 0], 6, [t 'lam.mu_l']);
0186 t_is(lam.mu_u, [0; 272; 0], 6, [t 'lam.mu_u']);
0187 t_is(lam.lower, [0; 0; 349.5; 4350], 5, [t 'lam.lower']);
0188 t_is(lam.upper, [0; 0; 0; 0], 7, [t 'lam.upper']);
0189 else
0190 t_skip(nmiqp, sprintf('%s does not handle MIQP problems', names{k}));
0191 end
0192
0193 end
0194 end
0195
0196 t_end;