[37] | 1 | function [prob,problem] = yalmip2geometric(options,F_struc,c,Q,K,ub,lb,mt,linear_variables,extended_variables); |
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| 2 | |
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| 3 | problem = 0; |
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| 4 | prob = []; |
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| 5 | h = []; |
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| 6 | A = []; % powers in objective/inequalities |
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| 7 | b = []; % coefficients in objective/inequalities |
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| 8 | G = []; % powers in equalities |
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| 9 | h = []; % coefficients in equalities |
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| 10 | |
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| 11 | % ********************************************************** |
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| 12 | % Initial sanity check for posynomial problem structure |
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| 13 | % ********************************************************** |
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| 14 | if any(ub<0) |
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| 15 | problem = -4; |
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| 16 | return |
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| 17 | end |
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| 18 | |
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| 19 | % ********************************************************** |
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| 20 | % Setup data related to objective |
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| 21 | % ********************************************************** |
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| 22 | vars_in_objective = find(c); |
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| 23 | A = mt(vars_in_objective,linear_variables); |
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| 24 | b = c(vars_in_objective); |
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| 25 | map_pos = 0; |
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| 26 | map = repmat(map_pos,length(b),1); |
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| 27 | |
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| 28 | % ********************************************************** |
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| 29 | % Invert negative monomial, or this is not a posynomial |
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| 30 | % ********************************************************** |
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| 31 | if any(b<0) |
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| 32 | if nnz(b)==1 |
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| 33 | b(find(b)) = -1/b(find(b)); |
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| 34 | A = -A; |
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| 35 | else |
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| 36 | problem = -4; |
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| 37 | return |
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| 38 | end |
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| 39 | end |
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| 40 | |
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| 41 | % ********************************************************** |
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| 42 | % Setup data related to inequalities sum(?x^?) > 0 |
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| 43 | % Loop through all inequalities, find the element with |
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| 44 | % positive coefficient, divide by this term. |
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| 45 | % ********************************************************** |
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| 46 | mte = blkdiag(0,mt); % Extend the monomial table with the monomial x^0 |
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| 47 | for j = 1+K.f:size(F_struc,1); |
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| 48 | k = find(F_struc(j,:)>0); |
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| 49 | if length(k) == 1 |
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| 50 | vars_in_c = find(F_struc(j,:)); |
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| 51 | Atemp = mte(vars_in_c,linear_variables+1); |
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| 52 | Atemp = Atemp - repmat(mte(k,linear_variables+1),size(Atemp,1),1); |
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| 53 | btemp = reshape(-F_struc(j,vars_in_c)/F_struc(j,k),length(vars_in_c),1); |
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| 54 | removed = find(sum(abs(Atemp),2)==0); |
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| 55 | Atemp(removed,:) = []; |
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| 56 | btemp(removed) = []; |
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| 57 | if length(btemp) > 0 |
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| 58 | A = [A;Atemp]; |
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| 59 | b = [b;btemp]; |
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| 60 | map_pos = map_pos + 1; |
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| 61 | % map = [map;repmat(map_pos,length(btemp),1)]; |
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| 62 | map = [map;map_pos*ones(length(btemp),1)]; |
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| 63 | end |
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| 64 | else |
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| 65 | if all(F_struc(j,:)>=0) |
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| 66 | % Redundant x+y > 1 |
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| 67 | elseif all(F_struc(j,:)<=0) |
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| 68 | % Infeasible x+y < -1 |
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| 69 | problem = 1; |
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| 70 | return |
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| 71 | % elseif F_struc(j,1)<0 & any(F_struc(j,2:end)<0) |
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| 72 | % % Trivially infeasible |
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| 73 | % problem = 1; |
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| 74 | % return |
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| 75 | else |
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| 76 | % Not posynomial at least |
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| 77 | problem = -4; |
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| 78 | return |
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| 79 | end |
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| 80 | end |
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| 81 | end |
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| 82 | |
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| 83 | % ********************************************************** |
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| 84 | % Fix equality constraints coming from fractional powers |
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| 85 | % of posynomials. |
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| 86 | % An equality constraint a(x) = t can be relaxed to a(x)<t |
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| 87 | % if only positive powers of t are used in the program. |
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| 88 | % NOTE : YALMIP defines these equalities as t-a(x)==0 |
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| 89 | % FIX : Is this check enough? |
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| 90 | % FIX : Speed things up... |
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| 91 | % ********************************************************** |
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| 92 | for j = 1:1:K.f |
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| 93 | k = find(F_struc(j,:)>0); |
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| 94 | if length(k)>1 |
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| 95 | error('Nonpositive terms in fractional expression in geometric program?') |
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| 96 | else |
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| 97 | if k==1 | ~ismember(k-1,extended_variables) |
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| 98 | % Monomial equality ok! |
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| 99 | else |
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| 100 | if all(A(:,find(ismember(linear_variables,k-1)))>=0) |
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| 101 | else |
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| 102 | error('Negative powers in fractional term in geometric program?') |
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| 103 | end |
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| 104 | end |
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| 105 | end |
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| 106 | end |
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| 107 | |
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| 108 | % ********************************************************** |
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| 109 | % Setup data related to inequalities derived from equalities |
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| 110 | % i.e. ax^b == 1 replaced with ax^b<1, (x^-b)/a < 1 |
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| 111 | % (except for extended variables according to above) |
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| 112 | % ********************************************************** |
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| 113 | for j = 1:1:K.f |
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| 114 | k = find(F_struc(j,:)>0); |
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| 115 | if length(k) == 1 |
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| 116 | vars_in_c = find(F_struc(j,:)); |
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| 117 | Atemp = mte(vars_in_c,linear_variables+1); |
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| 118 | Atemp = Atemp - repmat(mte(k,linear_variables+1),size(Atemp,1),1); |
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| 119 | btemp = reshape(-F_struc(j,vars_in_c)/F_struc(j,k),length(vars_in_c),1); |
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| 120 | removed = find(sum(abs(Atemp),2)==0); |
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| 121 | Atemp(removed,:) = []; |
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| 122 | btemp(removed) = []; |
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| 123 | |
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| 124 | if ~ismember(k-1,extended_variables) |
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| 125 | if length(btemp)==1 |
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| 126 | G = [G;Atemp]; |
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| 127 | h = [h;btemp]; |
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| 128 | else |
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| 129 | % a(x)+b(x) == c(x) not supported |
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| 130 | problem = -4; |
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| 131 | return |
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| 132 | end |
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| 133 | else |
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| 134 | % Just add upper inequalities |
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| 135 | A = [A;Atemp]; |
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| 136 | b = [b;btemp]; |
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| 137 | map_pos = map_pos + 1; |
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| 138 | this_map = repmat(map_pos,length(btemp),1); |
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| 139 | map = [map;this_map]; |
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| 140 | end |
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| 141 | else |
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| 142 | % a(x) < b(x) + c(x) not supported |
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| 143 | problem = -4; |
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| 144 | return |
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| 145 | end |
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| 146 | |
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| 147 | end |
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| 148 | |
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| 149 | % ********************************************************** |
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| 150 | % MOSEK does not like upper boud == lower bound |
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| 151 | % ********************************************************** |
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| 152 | if ~(isempty(lb) | isempty(ub)) |
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| 153 | fixed_variables = find(lb(linear_variables)==ub(linear_variables)); |
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| 154 | if ~isempty(fixed_variables) |
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| 155 | fixed_values = lb(linear_variables(fixed_variables)); |
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| 156 | if any(fixed_values==0) |
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| 157 | zeros_vars = find((lb(linear_variables)==ub(linear_variables)) & (lb(linear_variables)==0)); |
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| 158 | if any(A(:,zeros_vars)<0) |
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| 159 | problem = 1; |
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| 160 | return |
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| 161 | end |
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| 162 | end |
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| 163 | |
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| 164 | for i = 1:size(A,1) |
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| 165 | this_gain = 1; |
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| 166 | for j = 1:size(fixed_variables) |
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| 167 | this_gain = this_gain*fixed_values(j)^A(i,fixed_variables(j)); |
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| 168 | A(i,fixed_variables(j))=0; |
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| 169 | end |
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| 170 | b(i)=b(i)*this_gain; |
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| 171 | end |
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| 172 | end |
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| 173 | end |
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| 174 | if ~isempty(ub) |
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| 175 | for i = 1:length(ub(linear_variables)) |
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| 176 | if ~(isinf(ub(linear_variables(i))) | ub(linear_variables(i))==0) |
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| 177 | A(end+1,i) = 1; |
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| 178 | b(end+1) = 1/ub(linear_variables(i)); |
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| 179 | map_pos = map_pos + 1; |
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| 180 | map(end+1)=map_pos; |
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| 181 | end |
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| 182 | end |
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| 183 | end |
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| 184 | if ~isempty(lb) |
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| 185 | for i = 1:length(lb(linear_variables)) |
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| 186 | if ~(isinf(lb(linear_variables(i))) | lb(linear_variables(i))==0) |
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| 187 | A(end+1,i) = -1; |
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| 188 | b(end+1) = lb(linear_variables(i)); |
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| 189 | map_pos = map_pos + 1; |
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| 190 | map(end+1)=map_pos; |
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| 191 | end |
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| 192 | end |
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| 193 | end |
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| 194 | |
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| 195 | prob.b = b;prob.A = A;prob.map = map;prob.G = G;prob.h = h; |
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