0001 function t_mips(quiet)
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012 if nargin < 1
0013 quiet = 0;
0014 end
0015
0016 num_tests = 60;
0017
0018 t_begin(num_tests, quiet);
0019
0020 t = 'unconstrained banana function : ';
0021
0022 f_fcn = @(x)f2(x);
0023 x0 = [-1.9; 2];
0024
0025 [x, f, s, out, lam] = mips(f_fcn, x0);
0026 t_is(s, 1, 13, [t 'success']);
0027 t_is(x, [1; 1], 13, [t 'x']);
0028 t_is(f, 0, 13, [t 'f']);
0029 t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
0030 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0031 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0032 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0033 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0034
0035 t = 'unconstrained 3-d quadratic : ';
0036
0037 f_fcn = @(x)f3(x);
0038 x0 = [0; 0; 0];
0039
0040 [x, f, s, out, lam] = mips(f_fcn, x0);
0041 t_is(s, 1, 13, [t 'success']);
0042 t_is(x, [3; 5; 7], 13, [t 'x']);
0043 t_is(f, -244, 13, [t 'f']);
0044 t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
0045 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0046 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0047 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0048 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0049
0050 t = 'constrained 4-d QP : ';
0051
0052 f_fcn = @(x)f4(x);
0053 x0 = [1; 0; 0; 1];
0054 A = [ 1 1 1 1;
0055 0.17 0.11 0.10 0.18 ];
0056 l = [1; 0.10];
0057 u = [1; Inf];
0058 xmin = zeros(4,1);
0059
0060 [x, f, s, out, lam] = mips(f_fcn, x0, A, l, u, xmin);
0061 t_is(s, 1, 13, [t 'success']);
0062 t_is(x, [0; 2.8; 0.2; 0]/3, 6, [t 'x']);
0063 t_is(f, 3.29/3, 6, [t 'f']);
0064 t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
0065 t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
0066 t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
0067 t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
0068 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0069
0070
0071
0072
0073
0074
0075
0076
0077
0078
0079
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0084
0085 t = 'constrained 2-d nonlinear : ';
0086
0087 f_fcn = @(x)f5(x);
0088 gh_fcn = @(x)gh5(x);
0089 hess_fcn = @(x, lam, cost_mult)hess5(x, lam, cost_mult);
0090 x0 = [1.1; 0];
0091 xmin = zeros(2, 1);
0092
0093
0094 [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], xmin, [], gh_fcn, hess_fcn);
0095 t_is(s, 1, 13, [t 'success']);
0096 t_is(x, [1; 1], 6, [t 'x']);
0097 t_is(f, -2, 6, [t 'f']);
0098 t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
0099 t_is(lam.ineqnonlin, [0;0.5], 6, [t 'lam.ineqnonlin']);
0100 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0101 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0102 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0103 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0104
0105
0106
0107
0108
0109
0110
0111
0112
0113 t = 'constrained 3-d nonlinear : ';
0114
0115 f_fcn = @(x)f6(x);
0116 gh_fcn = @(x)gh6(x);
0117 hess_fcn = @(x, lam, cost_mult)hess6(x, lam, cost_mult);
0118 x0 = [1; 1; 0];
0119
0120 [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], [], [], gh_fcn, hess_fcn);
0121 t_is(s, 1, 13, [t 'success']);
0122 t_is(x, [1.58113883; 2.23606798; 1.58113883], 6, [t 'x']);
0123 t_is(f, -5*sqrt(2), 6, [t 'f']);
0124 t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
0125 t_is(lam.ineqnonlin, [0;sqrt(2)/2], 7, [t 'lam.ineqnonlin']);
0126 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0127 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0128 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0129 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0130
0131
0132
0133
0134
0135
0136
0137
0138
0139 t = 'constrained 3-d nonlinear (struct) : ';
0140 p = struct('f_fcn', f_fcn, 'x0', x0, 'gh_fcn', gh_fcn, 'hess_fcn', hess_fcn);
0141 [x, f, s, out, lam] = mips(p);
0142 t_is(s, 1, 13, [t 'success']);
0143 t_is(x, [1.58113883; 2.23606798; 1.58113883], 6, [t 'x']);
0144 t_is(f, -5*sqrt(2), 6, [t 'f']);
0145 t_is(out.hist(end).compcond, 0, 6, [t 'compcond']);
0146 t_is(lam.ineqnonlin, [0;sqrt(2)/2], 7, [t 'lam.ineqnonlin']);
0147 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0148 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0149 t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
0150 t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
0151
0152 t = 'constrained 4-d nonlinear : ';
0153
0154 f_fcn = @(x)f7(x);
0155 gh_fcn = @(x)gh7(x);
0156 hess_fcn = @(x, lam, sigma)hess7(x, lam, sigma);
0157 x0 = [1; 5; 5; 1];
0158 xmin = ones(4, 1);
0159 xmax = 5 * xmin;
0160
0161 [x, f, s, out, lam] = mips(f_fcn, x0, [], [], [], xmin, xmax, gh_fcn, hess_fcn);
0162 t_is(s, 1, 13, [t 'success']);
0163 t_is(x, [1; 4.7429994; 3.8211503; 1.3794082], 6, [t 'x']);
0164 t_is(f, 17.0140173, 6, [t 'f']);
0165 t_is(lam.eqnonlin, 0.1614686, 5, [t 'lam.eqnonlin']);
0166 t_is(lam.ineqnonlin, 0.55229366, 5, [t 'lam.ineqnonlin']);
0167 t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
0168 t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
0169 t_is(lam.lower, [1.08787121024; 0; 0; 0], 5, [t 'lam.lower']);
0170 t_is(lam.upper, zeros(size(x)), 7, [t 'lam.upper']);
0171
0172 t_end;
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0198
0199 function [f, df, d2f] = f2(x)
0200 a = 100;
0201 f = a*(x(2)-x(1)^2)^2+(1-x(1))^2;
0202 df = [ 4*a*(x(1)^3 - x(1)*x(2)) + 2*x(1)-2;
0203 2*a*(x(2) - x(1)^2) ];
0204 d2f = 4*a*[ 3*x(1)^2 - x(2) + 1/(2*a), -x(1);
0205 -x(1) 1/2 ];
0206
0207
0208
0209
0210 function [f, df, d2f] = f3(x)
0211 H = [5 -2 -1; -2 4 3; -1 3 5];
0212 c = [2; -35; -47];
0213 f = 1/2 * x'*H*x + c'*x + 5;
0214 df = H*x + c;
0215 d2f = H;
0216
0217
0218
0219
0220 function [f, df, d2f] = f4(x)
0221 H = [ 1003.1 4.3 6.3 5.9;
0222 4.3 2.2 2.1 3.9;
0223 6.3 2.1 3.5 4.8;
0224 5.9 3.9 4.8 10 ];
0225 c = zeros(4,1);
0226 f = 1/2 * x'*H*x + c'*x;
0227 df = H*x + c;
0228 d2f = H;
0229
0230
0231
0232
0233 function [f, df, d2f] = f5(x)
0234 c = -[1; 1];
0235 f = c'*x;
0236 df = c;
0237 d2f = zeros(2,2);
0238
0239 function [h, g, dh, dg] = gh5(x)
0240 h = [ -1 -1; 1 1] * x.^2 + [1; -2];
0241 dh = 2 * [-x(1) x(1); -x(2) x(2)];
0242 g = []; dg = [];
0243
0244 function Lxx = hess5(x, lam, cost_mult)
0245 mu = lam.ineqnonlin;
0246 Lxx = 2*[-1 1]*mu*eye(2);
0247
0248
0249
0250
0251 function [f, df, d2f] = f6(x)
0252 f = -x(1)*x(2) - x(2)*x(3);
0253 df = -[x(2); x(1)+x(3); x(2)];
0254 d2f = -[0 1 0; 1 0 1; 0 1 0];
0255
0256 function [h, g, dh, dg] = gh6(x)
0257 h = [ 1 -1 1; 1 1 1] * x.^2 + [-2; -10];
0258 dh = 2 * [x(1) x(1); -x(2) x(2); x(3) x(3)];
0259 g = []; dg = [];
0260
0261 function Lxx = hess6(x, lam, cost_mult)
0262 if nargin < 3, cost_mult = 1; end
0263 mu = lam.ineqnonlin;
0264 Lxx = cost_mult * [0 -1 0; -1 0 -1; 0 -1 0] + ...
0265 [2*[1 1]*mu 0 0; 0 2*[-1 1]*mu 0; 0 0 2*[1 1]*mu];
0266
0267
0268
0269
0270 function [f, df, d2f] = f7(x)
0271 f = x(1)*x(4)*sum(x(1:3)) + x(3);
0272 df = [ x(1)*x(4) + x(4)*sum(x(1:3));
0273 x(1)*x(4);
0274 x(1)*x(4) + 1;
0275 x(1)*sum(x(1:3)) ];
0276 d2f = sparse([ 2*x(4) x(4) x(4) 2*x(1)+x(2)+x(3);
0277 x(4) 0 0 x(1);
0278 x(4) 0 0 x(1);
0279 2*x(1)+x(2)+x(3) x(1) x(1) 0
0280 ]);
0281
0282 function [h, g, dh, dg] = gh7(x)
0283 g = sum(x.^2) - 40;
0284 h = -prod(x) + 25;
0285 dg = 2*x;
0286 dh = -prod(x)./x;
0287
0288 function Lxx = hess7(x, lam, sigma)
0289 if nargin < 3, sigma = 1; end
0290 lambda = lam.eqnonlin;
0291 mu = lam.ineqnonlin;
0292 [f, df, d2f] = f7(x);
0293 Lxx = sigma * d2f + lambda*2*speye(4) - ...
0294 mu*sparse([ 0 x(3)*x(4) x(2)*x(4) x(2)*x(3);
0295 x(3)*x(4) 0 x(1)*x(4) x(1)*x(3);
0296 x(2)*x(4) x(1)*x(4) 0 x(1)*x(2);
0297 x(2)*x(3) x(1)*x(3) x(1)*x(2) 0 ]);