1 | function output = mpcvx(p) |
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2 | %MPCVX Approximate multi-parametric programming |
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3 | % |
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4 | % MPCVX is never called by the user directly, but is called by |
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5 | % YALMIP from SOLVESDP, by choosing the solver tag 'mpcvx' in sdpsettings |
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6 | % |
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7 | % The behaviour of MPCVX can be altered using the fields |
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8 | % in the field 'mpcvx' in SDPSETTINGS |
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9 | % |
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10 | % WARNING: THIS IS EXPERIMENTAL CODE |
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11 | % |
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12 | |
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13 | % Author Johan Löfberg |
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14 | % $Id: mpcvx.m,v 1.6 2005/05/07 13:53:20 joloef Exp $ |
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15 | |
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16 | % ******************************** |
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17 | % INITIALIZE DIAGNOSTICS IN YALMIP |
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18 | % ******************************** |
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19 | mpsolvertime = clock; |
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20 | showprogress('mpcvx started',p.options.showprogress); |
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21 | |
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22 | % ******************************* |
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23 | % Display-logics |
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24 | % ******************************* |
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25 | switch max(min(p.options.verbose,3),0) |
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26 | case 0 |
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27 | p.options.bmibnb.verbose = 0; |
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28 | case 1 |
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29 | p.options.bmibnb.verbose = 1; |
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30 | p.options.verbose = 0; |
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31 | case 2 |
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32 | p.options.bmibnb.verbose = 2; |
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33 | p.options.verbose = 0; |
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34 | case 3 |
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35 | p.options.bmibnb.verbose = 2; |
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36 | p.options.verbose = 1; |
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37 | otherwise |
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38 | p.options.bmibnb.verbose = 0; |
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39 | p.options.verbose = 0; |
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40 | end |
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41 | |
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42 | % ******************************* |
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43 | % No reason to save |
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44 | % ******************************* |
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45 | p.options.saveduals = 0; |
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46 | |
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47 | % ********************************** |
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48 | % Generate an exploration set |
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49 | % ********************************** |
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50 | p.solver.subcall = 'callsedumi'; |
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51 | solver = eval(['@' p.solver.subcall]); % LP solver |
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52 | [THETA,problem] = ray_shoot(p,solver); |
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53 | |
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54 | %plot(polytope(THETA'));hold on; |
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55 | |
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56 | % ********************************** |
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57 | % Calculate optimal x in each initial vertex |
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58 | % ********************************** |
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59 | X = []; |
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60 | OBJ = []; |
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61 | for i = 1:size(THETA,2) |
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62 | [x_i,obj_i] = solve_node(p,solver,THETA(:,i)); |
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63 | X = [X x_i]; |
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64 | OBJ = [OBJ obj_i]; |
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65 | end |
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66 | |
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67 | % ********************************** |
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68 | % Partition initial set |
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69 | % ********************************** |
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70 | node_keeper; |
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71 | node_keeper(THETA,X,OBJ); |
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72 | T = delaunayn(THETA',{'Qz','Qt'}); |
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73 | |
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74 | % ********************************** |
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75 | % Do algo on all initial simplicies |
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76 | % ********************************** |
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77 | optimal_simplicies = []; |
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78 | p.options.mpcvx.eps = 5e-2; |
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79 | for i = 1:size(T,1) |
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80 | optimal_simplicies = [optimal_simplicies mp_simplex(p,solver,T(i,:)')]; |
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81 | end |
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82 | mpsolvertime = etime(clock,mpsolvertime) |
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83 | |
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84 | % ********************************** |
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85 | % Create format compatible with MPT |
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86 | % ********************************** |
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87 | Pn = polytope; |
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88 | j = 1; |
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89 | for i = 1:size(optimal_simplicies,2) |
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90 | [theta,x,obj] = node_keeper(optimal_simplicies(:,i)); |
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91 | m = size(theta,1); |
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92 | Minv = inv([ones(1,m+1);theta]); |
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93 | |
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94 | try |
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95 | Pn = [Pn polytope(theta')]; |
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96 | Gi{j} = x(find(~ismember(1:length(p.c),p.parametric_variables)),:)*Minv(:,1); |
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97 | Fi{j} = x(find(~ismember(1:length(p.c),p.parametric_variables)),:)*Minv(:,2:end); |
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98 | j = j + 1; |
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99 | catch |
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100 | %Gi{j} = polytope([]); |
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101 | %Fi{j} = polytope([]); |
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102 | end |
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103 | end |
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104 | |
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105 | output.problem = problem; |
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106 | output.Primal = nan*ones(length(p.c),1); |
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107 | output.Dual = []; |
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108 | output.Slack = []; |
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109 | output.infostr = yalmiperror(output.problem,'MPCVX'); |
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110 | output.solverinput = 0; |
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111 | output.solveroutput.Pn = Pn; |
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112 | output.solveroutput.Fi = Fi; |
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113 | output.solveroutput.Gi = Gi; |
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114 | output.solvertime = mpsolvertime; |
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115 | |
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116 | function simplex_solution = mp_simplex(p,solver,theta_indicies) |
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117 | |
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118 | [theta,x,obj] = node_keeper(theta_indicies); |
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119 | % Parametric dimension |
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120 | m = size(theta,1); |
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121 | |
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122 | Minv = inv([ones(1,m+1);theta]); |
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123 | M1 = Minv(:,1); |
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124 | M2 = zeros(size(M1,1),length(p.c)); |
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125 | M2(:,p.parametric_variables) = Minv(:,2:end); |
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126 | p.F_struc = [M1 M2;p.F_struc]; |
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127 | p.K.l = p.K.l + size(M1,1); |
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128 | |
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129 | Vbar = obj'*Minv; |
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130 | c = p.c; |
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131 | c2 = zeros(length(p.c),1);c2(p.parametric_variables) = -Vbar(2:end); |
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132 | p.c = p.c+c2;p.c; |
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133 | output = feval(solver,p); |
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134 | p.c = c; |
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135 | |
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136 | upper = obj'*Minv*[1;output.Primal(p.parametric_variables)]; |
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137 | lower = p.c'*output.Primal+output.Primal'*p.Q*output.Primal; |
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138 | |
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139 | eps_CP_S = min(upper-lower,((upper-lower)/(1+lower))); |
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140 | |
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141 | % Dig deeper? |
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142 | %plot(polytope(theta'),struct('color',rand(3,1))) |
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143 | if eps_CP_S > p.options.mpcvx.eps |
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144 | |
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145 | thetac = output.Primal(p.parametric_variables); |
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146 | |
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147 | [x_i,obj_i] = solve_node(p,solver,thetac); |
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148 | new_index = node_keeper(thetac(:),x_i(:),obj_i); |
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149 | |
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150 | simplex_solution = []; |
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151 | for i = 1:(size(theta,1)+1) |
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152 | j = 1:(size(theta,1)+1); |
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153 | j(i)=[]; |
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154 | theta_test = [theta(:,j) thetac]; |
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155 | if min(svd([ones(1,size(theta_test,2));theta_test]))>1e-4 |
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156 | simplex_solution = [simplex_solution mp_simplex(p,solver,[theta_indicies(j);new_index])]; |
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157 | end |
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158 | end |
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159 | |
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160 | else |
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161 | % This simplex constitutes a node, report back |
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162 | simplex_solution = theta_indicies(:); |
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163 | end |
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164 | |
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165 | function varargout = node_keeper(varargin) |
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166 | |
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167 | persistent savedTHETA |
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168 | persistent savedX |
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169 | persistent savedOBJ |
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170 | |
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171 | switch nargin |
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172 | case 0 % CLEAR |
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173 | savedTHETA = []; |
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174 | savedX = []; |
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175 | savedOBJ = []; |
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176 | case 3 % Append |
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177 | savedTHETA = [savedTHETA varargin{1}]; |
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178 | savedX = [savedX varargin{2}]; |
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179 | savedOBJ = [savedOBJ varargin{3}]; |
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180 | varargout{1} = size(savedTHETA,2); |
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181 | case 1 % Get data |
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182 | varargout{1} = savedTHETA(:,varargin{1}); |
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183 | varargout{2} = savedX(:,varargin{1}); |
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184 | varargout{3} = savedOBJ(:,varargin{1});varargout{3} = varargout{3}(:); |
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185 | otherwise |
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186 | error('!') |
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187 | end |
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188 | |
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189 | |
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190 | function [THETA,problem] = ray_shoot(p,solver) |
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191 | THETA = []; |
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192 | |
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193 | p_temp = p; |
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194 | p_temp.c = p_temp.c*0; |
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195 | p_temp.Q = 0*p_temp.Q; |
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196 | for i = 1:25 |
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197 | p_temp.c(p.parametric_variables) = randn(length(p.parametric_variables),1); |
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198 | output = feval(solver,p_temp); |
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199 | THETA = [THETA output.Primal(p.parametric_variables)]; |
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200 | end |
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201 | % Select unique and generate center |
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202 | THETA = unique(fix(THETA'*1e4)/1e4,'rows')'; |
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203 | center = sum(THETA,2)/size(THETA,2); |
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204 | THETA = [THETA*0.999+repmat(0.001*center,1,size(THETA,2))]; |
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205 | problem = 0; |
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206 | |
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207 | |
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208 | function [x_i,obj_i] = solve_node(p,solver,theta); |
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209 | p_temp = p; |
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210 | p_temp.F_struc(:,1) = p_temp.F_struc(:,1) + p_temp.F_struc(:,1+p.parametric_variables)*theta; |
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211 | p_temp.F_struc(:,1+p.parametric_variables) = []; |
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212 | |
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213 | empty_rows = find(~any(p_temp.F_struc(p.K.f+1:p.K.f+p.K.l,2:end),2)); |
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214 | if ~isempty(empty_rows) |
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215 | if all(p_temp.F_struc(p.K.f+empty_rows,1)>=-1e-7) |
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216 | p_temp.F_struc(p.K.f+empty_rows,:)=[]; |
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217 | p_temp.K.l = p_temp.K.l - length(empty_rows); |
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218 | else |
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219 | feasible = 0; |
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220 | end |
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221 | end |
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222 | |
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223 | x_var = find(~ismember(1:length(p.c),p.parametric_variables)); |
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224 | theta_var = p.parametric_variables; |
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225 | Q11 = p.Q(x_var,x_var); |
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226 | Q12 = p.Q(x_var,theta_var); |
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227 | Q22 = p.Q(theta_var,theta_var); |
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228 | c1 = p.c(x_var); |
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229 | c2 = p.c(theta_var); |
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230 | |
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231 | p_temp.Q = Q11; |
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232 | p_temp.c = c1+2*Q12*theta; |
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233 | |
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234 | %p_temp.c(p.parametric_variables) = []; |
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235 | %p_temp.Q(:,p.parametric_variables) = []; |
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236 | %p_temp.Q(p.parametric_variables,:) = []; |
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237 | output = feval(solver,p_temp); |
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238 | |
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239 | % Recover complete [x theta] |
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240 | x_i = zeros(length(p.c),1); |
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241 | x_i(find(~ismember(1:length(p.c),p.parametric_variables))) = output.Primal; |
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242 | x_i(p.parametric_variables) = theta; |
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243 | obj_i = x_i'*p.Q*x_i+p.c'*x_i; |
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