[37] | 1 | function [F,h,failure] = robustify(F,h,ops,w) |
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| 2 | %ROBUSTIFY Derives robust counterpart. |
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| 3 | % |
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| 4 | % [Frobust,objrobust,failure] = ROBUSTIFY(F,h,options) is used to derive |
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| 5 | % the robust counterpart of an uncertain YALMIP model. |
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| 6 | % |
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| 7 | % min h(x,w) |
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| 8 | % subject to |
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| 9 | % F(x,w) >(=) 0 for all w in W |
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| 10 | % |
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| 11 | % The constraints and objective have to satisfy a number of conditions for |
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| 12 | % the robustification to be tractable. Please refer to the YALMIP Wiki for |
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| 13 | % the current assumptions (this is constantly developing) |
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| 14 | % |
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| 15 | % See also SOLVEROBUST, UNCERTAIN |
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| 16 | |
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| 17 | % Author Johan Löfberg |
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| 18 | % $Id: robustify.m,v 1.19 2006/10/24 12:02:04 joloef Exp $ |
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| 19 | |
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| 20 | if nargin < 3 |
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| 21 | ops = []; |
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| 22 | end |
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| 23 | |
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| 24 | if nargin < 4 |
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| 25 | w = []; |
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| 26 | end |
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| 27 | |
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| 28 | if isempty(w) |
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| 29 | unc_declarations = is(F,'uncertain'); |
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| 30 | if any(unc_declarations) |
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| 31 | w = recover(getvariables(sdpvar(F(find(unc_declarations))))); |
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| 32 | F = F(find(~unc_declarations)); |
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| 33 | else |
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| 34 | error('There is no uncertainty definition in the model.') |
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| 35 | end |
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| 36 | end |
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| 37 | |
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| 38 | if isempty(ops) |
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| 39 | ops = sdpsettings; |
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| 40 | end |
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| 41 | |
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| 42 | % Figure out which variables are uncertain, certain, and lifted variables |
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| 43 | % in the uncertainty description (this code is buggy as ....) |
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| 44 | [x,w,x_variables,w_variables,aux_variables,F,failure] = robust_classify_variables(F,h,ops,w); |
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| 45 | if failure |
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| 46 | return |
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| 47 | end |
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| 48 | |
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| 49 | % Integer variables are OK in x, but not in the uncertainty (robustification |
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| 50 | % is based on strong duality in w-space) |
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| 51 | integervars = [yalmip('binvariables') yalmip('intvariables')]; |
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| 52 | ind = find(is(F,'integer') | is(F,'binary')); |
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| 53 | if ~isempty(ind) |
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| 54 | integervars = [integervars getvariables(F(ind))]; |
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| 55 | if any(ismember(w_variables,integervars)) |
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| 56 | failure = 1; |
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| 57 | return |
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| 58 | end |
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| 59 | end |
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| 60 | |
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| 61 | % Find uncertainty description, uncertain and certain constraints |
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| 62 | F_w = set([]); |
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| 63 | F_x = set([]); |
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| 64 | F_xw = set([]); |
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| 65 | for i = 1:length(F) |
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| 66 | if all(ismember(depends(F(i)),w_variables)) |
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| 67 | % Uncertainty definition |
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| 68 | F_w = F_w + F(i); |
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| 69 | elseif all(ismember(depends(F(i)),x_variables)) |
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| 70 | % Certain constraint |
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| 71 | F_x = F_x + F(i); |
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| 72 | else |
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| 73 | % Uncertain constraint |
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| 74 | F_xw = F_xw + F(i); |
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| 75 | end |
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| 76 | end |
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| 77 | |
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| 78 | % Limitation in the modelling language... |
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| 79 | if ~isempty(intersect(intersect(depends(F_xw),depends(F_w)),aux_variables)) |
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| 80 | disp('You are most likely using a nonlinear operator to describe the'); |
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| 81 | disp('uncertainty set (such as norm(w,1) <=1). This is currently not'); |
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| 82 | disp('supported. Please model the constraint manually.'); |
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| 83 | error('Uncertain model does not satisfy assumptions (nonlinear operator on uncertainty in uncertain constraint)'); |
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| 84 | end |
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| 85 | |
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| 86 | if length(F_w)==0 |
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| 87 | error('There is no uncertainty description in the model.'); |
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| 88 | end |
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| 89 | |
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| 90 | % Some pre-calc |
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| 91 | xw = [x;w]; |
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| 92 | xind = find(ismembc(getvariables(xw),getvariables(x))); |
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| 93 | wind = find(ismembc(getvariables(xw),getvariables(w))); |
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| 94 | % Analyze the objective and try to rewrite any uncertainty into the format |
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| 95 | % assumed by YALMIP ( |
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| 96 | if ~isempty(h) |
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| 97 | % |
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| 98 | %[Q,c,f] = quadratic_model(h,xw); |
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| 99 | if 0 |
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| 100 | [Q,c,f,dummy,nonquadratic] = quaddecomp(h,xw); |
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| 101 | else |
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| 102 | [Q,c,f,dummy,nonquadratic] = vecquaddecomp(h,xw); |
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| 103 | Q = Q{1}; |
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| 104 | c = c{1}; |
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| 105 | f = f{1}; |
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| 106 | end |
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| 107 | if nonquadratic |
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| 108 | error('Objective can be at most quadratic, with the linear term uncertain'); |
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| 109 | end |
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| 110 | Q_ww = Q(wind,wind); |
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| 111 | Q_xw = Q(xind,wind); |
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| 112 | Q_xx = Q(xind,xind); |
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| 113 | c_x = c(xind); |
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| 114 | c_w = c(wind); |
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| 115 | |
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| 116 | if nnz(Q_ww) > 0 |
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| 117 | error('Objective can be at most quadratic, with the linear term uncertain'); |
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| 118 | end |
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| 119 | % Separate certain and uncertain terms, place uncertain terms in the |
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| 120 | % constraints instead |
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| 121 | if is(h,'linear') |
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| 122 | if isempty(intersect(getvariables(w),getvariables(h))) |
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| 123 | h_fixed = h; |
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| 124 | else |
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| 125 | sdpvar t |
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| 126 | F_xw = F_xw + set(h < t); |
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| 127 | h_fixed = t; |
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| 128 | x = [x;t]; |
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| 129 | end |
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| 130 | else |
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| 131 | h_fixed = x'*Q_xx*x + c_x'*x + f; |
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| 132 | h_uncertain = 2*w'*Q_xw'*x + c_w'*w; |
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| 133 | if ~isa(h_uncertain,'double') |
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| 134 | sdpvar t |
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| 135 | F_xw = F_xw + set(h_uncertain < t); |
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| 136 | h_fixed = h_fixed + t; |
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| 137 | x = [x;t]; |
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| 138 | end |
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| 139 | end |
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| 140 | else |
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| 141 | h_fixed = []; |
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| 142 | end |
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| 143 | |
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| 144 | % Convert quadratic constraints in uncertainty model to SOCPs. |
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| 145 | F_w = convertquadratics(F_w); |
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| 146 | |
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| 147 | % Export uncertainty model to numerical format |
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| 148 | ops.solver = ''; |
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| 149 | [aux1,aux2,aux3,Zmodel] = export(F_w,[],ops,[],[],1); |
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| 150 | |
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| 151 | if ~isempty(Zmodel) |
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| 152 | if length(Zmodel.c) ~= length(w) |
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| 153 | error('Some uncertain variables are unconstrained.') |
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| 154 | end |
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| 155 | else |
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| 156 | error('Failed when exporting a model of the uncertainty.') |
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| 157 | end |
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| 158 | |
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| 159 | % OK, we are done with the initial analysis of the involved variables, and |
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| 160 | % check of the objective function. |
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| 161 | % |
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| 162 | % At this point, we apply algorithms to robustify constraints (currently we |
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| 163 | % only have code for the uncertain conic LP case and polytopic SDP) |
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| 164 | |
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| 165 | F_robust = set([]); |
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| 166 | |
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| 167 | % Pick out the uncertain linear equalities and robustify |
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| 168 | F_lp = F_xw(find(is(F_xw,'elementwise'))); |
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| 169 | F_xw = F_xw - F_lp; |
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| 170 | F_robust = F_robust + robustify_lp_conic(F_lp,Zmodel,x,w); |
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| 171 | |
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| 172 | % Pick out uncertain SOCP & SDP constraints and robustify |
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| 173 | F_sdp = F_xw(find(is(F_xw,'sdp') | is(F_xw,'socc'))); |
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| 174 | F_xw = F_xw - F_sdp; |
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| 175 | F_robust = F_robust + robustify_sdp_conic(F_sdp,Zmodel,x,w); |
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| 176 | |
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| 177 | % Pick out the uncertain equalities and robustify |
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| 178 | F_eq = F_xw(find(is(F_xw,'equality'))); |
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| 179 | F_xw = F_xw - F_eq; |
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| 180 | F_robust = F_robust + robustify_eq_conic(F_eq,Zmodel,x,w); |
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| 181 | |
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| 182 | |
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| 183 | if length(F_xw) > 0 |
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| 184 | error('There are some uncertain constraints that not are supported by YALMIP') |
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| 185 | end |
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| 186 | |
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| 187 | % Return the robustfied model |
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| 188 | F = F_robust+F_x; |
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| 189 | h = h_fixed; |
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| 190 | |
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| 191 | % The model has been expanded, so we have to remember this (trying to |
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| 192 | % expand an expanded model leads to nonconvexity error) |
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| 193 | F = expanded(F,1); % This is actually done already in expandmodel |
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| 194 | h = expanded(h,1); % But this one has to be done manually |
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