232 lines
7.3 KiB
Mathematica
232 lines
7.3 KiB
Mathematica
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function [prob,problem] = yalmip2geometric(options,F_struc,c,Q,K,ub,lb,mt,linear_variables,extended_variables);
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problem = 0;
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prob = [];
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h = [];
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A = []; % powers in objective/inequalities
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b = []; % coefficients in objective/inequalities
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G = []; % powers in equalities
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h = []; % coefficients in equalities
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% **********************************************************
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% Initial sanity check for posynomial problem structure
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% **********************************************************
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if any(ub<0)
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problem = -8;
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return
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end
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% **********************************************************
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% Wrong quadratic (negative terms)
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% Fix: Add code for the case min -x1*x2 ===> min 1/x1x2
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% **********************************************************
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if any(any(Q<0))
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problem = -8;
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return
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end
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% **********************************************************
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% Setup data related to objective
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% **********************************************************
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vars_in_objective = find(c);
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A = mt(vars_in_objective,linear_variables);
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b = c(vars_in_objective);
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map_pos = 0;
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map = repmat(map_pos,length(b),1);
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% **********************************************************
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% Invert negative monomial, or this is not a posynomial
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% **********************************************************
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if any(b<0)
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if nnz(b)==1
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b(find(b)) = -1/b(find(b));
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A = -A;
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else
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problem = -8;
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return
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end
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end
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% **********************************************************
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% Setup data related to inequalities sum(?x^?) > 0
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% Loop through all inequalities, find the element with
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% positive coefficient, divide by this term.
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% **********************************************************
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mte = blkdiag(0,mt); % Extend the monomial table with the monomial x^0
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% These are strange, either trivial or not posynomials (multiple terms have
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% positive coefficients, such as 1 -x + y > 0 or x + y > 0)
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k = find((sum(F_struc(1+K.f:end,:)>0,2))>1);
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if ~isempty(k)
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for j = k(:)'
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if all(F_struc(j,:)>=0)
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% Redundant x+y > -something
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elseif all(F_struc(j,:)<=0)
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% Infeasible x+y < -1
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problem = 1;
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return
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else
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% Not posynomial at least
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problem = -8;
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return
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end
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end
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end
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% remove those redundant constraints
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F_struc(K.f + k,:)=[];
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k = [];
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if any(F_struc(:,1) < 0 & all(F_struc(:,2:end)<=0,2))
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% This is something like x + y < -1
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problem = 1;
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return;
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end
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% horribly hacked to avoid FIND and sparse subsref inside the loop
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% FIXME: Assumes no constraints of the type x + y < 0
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ss = full([F_struc > 0]*[(1:size(F_struc,2))]');
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[all_non_zeros,temp,vals] = find(F_struc(1+K.f:end,:)');
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pos_vals = (vals(vals>0));
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nnz_per_row = sum(F_struc~=0,2);
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index = 1;
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A = A';
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map = map';
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for j = setdiff(1+K.f:size(F_struc,1),k)
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k = ss(j);
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vars_in_c = all_non_zeros(index:index + nnz_per_row(j) - 1)';
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Atemp = mte(vars_in_c,linear_variables+1);
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Atemp = Atemp - repmat(mte(k,linear_variables+1),size(Atemp,1),1);
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% f = F_struc(j,:);
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% btemp = reshape(-f(vars_in_c)/f(k),length(vars_in_c),1);
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btemp = reshape(-vals(index:index + nnz_per_row(j) - 1)/pos_vals(1),length(vars_in_c),1);
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% btemp = reshape(-vals(index:index + nnz_per_row(j) - 1)/pos_vals(k),length(vars_in_c),1);
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removed = find(sum(abs(Atemp),2)==0);
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Atemp(removed,:) = [];
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btemp(removed) = [];
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index = index + nnz_per_row(j);
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pos_vals(1)=[];
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if length(btemp) > 0
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A = [A Atemp'];
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b = [b;full(btemp)];
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map_pos = map_pos + 1;
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map = [map map_pos*ones(1,length(btemp))];
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end
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end
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map = map';
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A = A';
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% **********************************************************
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% Fix equality constraints coming from fractional powers
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% of posynomials.
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% An equality constraint a(x) = t can be relaxed to a(x)<t
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% if only positive powers of t are used in the program.
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% NOTE : YALMIP defines these equalities as t-a(x)==0
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% FIX : Is this check enough?
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% FIX : Speed things up...
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% **********************************************************
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for j = 1:1:K.f
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k = find(F_struc(j,:)>0);
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if length(k)>1
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problem = -8;
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return
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else
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if k==1 | ~ismember(k-1,extended_variables)
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% Monomial equality ok!
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else
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if all(A(:,find(ismember(linear_variables,k-1)))>=0)
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else
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problem = -8;
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return
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end
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end
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end
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end
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% **********************************************************
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% Setup data related to inequalities derived from equalities
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% i.e. ax^b == 1 replaced with ax^b<1, (x^-b)/a < 1
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% (except for extended variables according to above)
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% **********************************************************
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for j = 1:1:K.f
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k = find(F_struc(j,:)>0);
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if length(k) == 1
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vars_in_c = find(F_struc(j,:));
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Atemp = mte(vars_in_c,linear_variables+1);
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Atemp = Atemp - repmat(mte(k,linear_variables+1),size(Atemp,1),1);
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btemp = reshape(-F_struc(j,vars_in_c)/F_struc(j,k),length(vars_in_c),1);
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removed = find(sum(abs(Atemp),2)==0);
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Atemp(removed,:) = [];
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btemp(removed) = [];
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if ~ismember(k-1,extended_variables)
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if length(btemp)==1
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G = [G;Atemp];
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h = [h;btemp];
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else
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% a(x)+b(x) == c(x) not supported
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problem = -4;
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return
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end
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else
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% Just add upper inequalities
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A = [A;Atemp];
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b = [b;btemp];
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map_pos = map_pos + 1;
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this_map = repmat(map_pos,length(btemp),1);
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map = [map;this_map];
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end
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else
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% a(x) < b(x) + c(x) not supported
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problem = -4;
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return
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end
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end
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% **********************************************************
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% MOSEK does not like upper boud == lower bound
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% **********************************************************
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if ~(isempty(lb) | isempty(ub))
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fixed_variables = find(lb(linear_variables)==ub(linear_variables));
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if ~isempty(fixed_variables)
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fixed_values = lb(linear_variables(fixed_variables));
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if any(fixed_values==0)
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zeros_vars = find((lb(linear_variables)==ub(linear_variables)) & (lb(linear_variables)==0));
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if any(A(:,zeros_vars)<0)
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problem = 1;
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return
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end
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end
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for i = 1:size(A,1)
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this_gain = 1;
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for j = 1:size(fixed_variables)
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this_gain = this_gain*fixed_values(j)^A(i,fixed_variables(j));
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A(i,fixed_variables(j))=0;
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end
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b(i)=b(i)*this_gain;
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end
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end
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end
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if ~isempty(ub)
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for i = 1:length(ub(linear_variables))
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if ~(isinf(ub(linear_variables(i))) | ub(linear_variables(i))==0)
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A(end+1,i) = 1;
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b(end+1) = 1/ub(linear_variables(i));
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map_pos = map_pos + 1;
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map(end+1)=map_pos;
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end
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end
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end
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if ~isempty(lb)
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for i = 1:length(lb(linear_variables))
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if ~(isinf(lb(linear_variables(i))) | lb(linear_variables(i))==0)
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A(end+1,i) = -1;
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b(end+1) = lb(linear_variables(i));
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map_pos = map_pos + 1;
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map(end+1)=map_pos;
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end
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end
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end
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prob.b = b;prob.A = A;prob.map = map;prob.G = G;prob.h = h;
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