0001 function t_qps_matpower(quiet)
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012 if nargin < 1
0013 quiet = 0;
0014 end
0015
0016 algs = {'BPMPD', 'MIPS', 250, 'IPOPT', 'OT', 'CPLEX', 'MOSEK', 'GUROBI', 'CLP', 'GLPK'};
0017 names = {'BPMPD_MEX', 'MIPS', 'sc-MIPS', 'IPOPT', 'linprog/quadprog', 'CPLEX', 'MOSEK', 'Gurobi', 'CLP', 'glpk'};
0018 check = {'bpmpd', [], [], 'ipopt', 'quadprog', 'cplex', 'mosek', 'gurobi', 'clp', 'glpk'};
0019 does_qp = [1 1 1 1 1 1 1 1 1 0];
0020
0021 n = 36;
0022 nqp = 28;
0023 t_begin(n*length(algs), quiet);
0024
0025 diff_alg_warn_id = 'optim:linprog:WillRunDiffAlg';
0026 if have_fcn('quadprog') && have_fcn('quadprog', 'vnum') == 7.005
0027 s1 = warning('query', diff_alg_warn_id);
0028 warning('off', diff_alg_warn_id);
0029 end
0030
0031 for k = 1:length(algs)
0032 if ~isempty(check{k}) && ~have_fcn(check{k})
0033 t_skip(n, sprintf('%s not installed', names{k}));
0034 else
0035 opt = struct('verbose', 0, 'alg', algs{k});
0036 if strcmp(names{k}, 'MIPS') || strcmp(names{k}, 'sc-MIPS')
0037 opt.mips_opt.comptol = 1e-8;
0038 end
0039
0040
0041
0042
0043
0044
0045
0046 if strcmp(names{k}, 'CPLEX')
0047
0048 alg = 2;
0049 mpopt = mpoption('cplex.lpmethod', alg, 'cplex.qpmethod', min([4 alg]));
0050 opt.cplex_opt = cplex_options([], mpopt);
0051 end
0052 if strcmp(names{k}, 'MOSEK')
0053 mpopt = mpoption;
0054
0055
0056
0057
0058 mpopt = mpoption(mpopt, 'mosek.gap_tol', 1e-10);
0059
0060
0061
0062
0063 vnum = have_fcn('mosek', 'vnum');
0064 if vnum >= 8
0065
0066
0067
0068
0069 mpopt = mpoption(mpopt, 'mosek.opts.MSK_DPAR_INTPNT_QO_TOL_REL_GAP', 1e-10);
0070 end
0071
0072 opt.mosek_opt = mosek_options([], mpopt);
0073 end
0074
0075 t = sprintf('%s - 3-d LP : ', names{k});
0076
0077 c = [-5; -4; -6];
0078 A = [1 -1 1;
0079 -3 -2 -4;
0080 3 2 0];
0081 l = [-Inf; -42; -Inf];
0082 u = [20; Inf; 30];
0083 xmin = [0; 0; 0];
0084 x0 = [];
0085 [x, f, s, out, lam] = qps_matpower([], c, A, l, u, xmin, [], [], opt);
0086 t_is(s, 1, 12, [t 'success']);
0087 t_is(x, [0; 15; 3], 6, [t 'x']);
0088 t_is(f, -78, 6, [t 'f']);
0089 t_is(lam.mu_l, [0;1.5;0], 9, [t 'lam.mu_l']);
0090 t_is(lam.mu_u, [0;0;0.5], 9, [t 'lam.mu_u']);
0091 if strcmp(algs{k}, 'CLP') && ~have_fcn('opti_clp')
0092 t_skip(2, [t 'lam.lower/upper : MEXCLP does not return multipliers on var bounds']);
0093 else
0094 t_is(lam.lower, [1;0;0], 9, [t 'lam.lower']);
0095 t_is(lam.upper, zeros(size(x)), 9, [t 'lam.upper']);
0096 end
0097
0098 if does_qp(k)
0099 t = sprintf('%s - unconstrained 3-d quadratic : ', names{k});
0100
0101 H = [5 -2 -1; -2 4 3; -1 3 5];
0102 c = [2; -35; -47];
0103 x0 = [0; 0; 0];
0104 [x, f, s, out, lam] = qps_matpower(H, c, [], [], [], [], [], [], opt);
0105 t_is(s, 1, 12, [t 'success']);
0106 t_is(x, [3; 5; 7], 8, [t 'x']);
0107 t_is(f, -249, 13, [t 'f']);
0108 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0109 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0110 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0111 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0112
0113 t = sprintf('%s - constrained 2-d QP : ', names{k});
0114
0115 H = [ 1 -1;
0116 -1 2 ];
0117 c = [-2; -6];
0118 A = [ 1 1;
0119 -1 2;
0120 2 1 ];
0121 l = [];
0122 u = [2; 2; 3];
0123 xmin = [0; 0];
0124 x0 = [];
0125 [x, f, s, out, lam] = qps_matpower(H, c, A, l, u, xmin, [], x0, opt);
0126 t_is(s, 1, 12, [t 'success']);
0127 t_is(x, [2; 4]/3, 7, [t 'x']);
0128 t_is(f, -74/9, 6, [t 'f']);
0129 t_is(lam.mu_l, [0;0;0], 13, [t 'lam.mu_l']);
0130 t_is(lam.mu_u, [28;4;0]/9, 4, [t 'lam.mu_u']);
0131 if strcmp(algs{k}, 'CLP') && ~have_fcn('opti_clp')
0132 t_skip(2, [t 'lam.lower/upper : MEXCLP does not return multipliers on var bounds']);
0133 else
0134 t_is(lam.lower, zeros(size(x)), 7, [t 'lam.lower']);
0135 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0136 end
0137
0138 t = sprintf('%s - constrained 4-d QP : ', names{k});
0139
0140 H = [ 1003.1 4.3 6.3 5.9;
0141 4.3 2.2 2.1 3.9;
0142 6.3 2.1 3.5 4.8;
0143 5.9 3.9 4.8 10 ];
0144 c = zeros(4,1);
0145 A = [ 1 1 1 1;
0146 0.17 0.11 0.10 0.18 ];
0147 l = [1; 0.10];
0148 u = [1; Inf];
0149 xmin = zeros(4,1);
0150 x0 = [1; 0; 0; 1];
0151 [x, f, s, out, lam] = qps_matpower(H, c, A, l, u, xmin, [], x0, opt);
0152 t_is(s, 1, 12, [t 'success']);
0153 t_is(x, [0; 2.8; 0.2; 0]/3, 5, [t 'x']);
0154 t_is(f, 3.29/3, 6, [t 'f']);
0155 t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
0156 t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
0157 if strcmp(algs{k}, 'CLP') && ~have_fcn('opti_clp')
0158 t_skip(2, [t 'lam.lower/upper : MEXCLP does not return multipliers on var bounds']);
0159 else
0160 t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
0161 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0162 end
0163
0164 t = sprintf('%s - (struct) constrained 4-d QP : ', names{k});
0165 p = struct('H', H, 'A', A, 'l', l, 'u', u, 'xmin', xmin, 'x0', x0, 'opt', opt);
0166 [x, f, s, out, lam] = qps_matpower(p);
0167 t_is(s, 1, 12, [t 'success']);
0168 t_is(x, [0; 2.8; 0.2; 0]/3, 5, [t 'x']);
0169 t_is(f, 3.29/3, 6, [t 'f']);
0170 t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
0171 t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
0172 if strcmp(algs{k}, 'CLP') && ~have_fcn('opti_clp')
0173 t_skip(2, [t 'lam.lower/upper : MEXCLP does not return multipliers on var bounds']);
0174 else
0175 t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
0176 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0177 end
0178 else
0179 t_skip(nqp, sprintf('%s does not handle QP problems', names{k}));
0180 end
0181
0182 t = sprintf('%s - infeasible LP : ', names{k});
0183 p = struct('A', sparse([1 1]), 'c', [1;1], 'u', -1, 'xmin', [0;0], 'opt', opt);
0184 [x, f, s, out, lam] = qps_matpower(p);
0185 t_ok(s <= 0, [t 'no success']);
0186 end
0187 end
0188
0189 if have_fcn('quadprog') && have_fcn('quadprog', 'vnum') == 7.005
0190 warning(s1.state, diff_alg_warn_id);
0191 end
0192
0193 t_end;