210 lines
6.1 KiB
Mathematica
210 lines
6.1 KiB
Mathematica
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function diagnostic = bisection_core(Constraints,Objective,options)
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%BISECTION Core engine
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% Note, outer layer added to enable arbitrary sign on ojective.
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% Code here initially assumed maximization of scalar, so now we tweak the
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% code a bit with swtchedsign to run any case. Fugly.
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diagnostic.yalmiptime = 0;
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diagnostic.solvertime = 0;
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diagnostic.info = '';
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diagnostic.problem = 0;
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the_sign = 1;
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if options.bisection.switchedsign
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the_sign = -1;
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end
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if length(getvariables(Objective)) > 1
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diagnostic.problem = -4;
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return
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end
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if ~(isequal(getbase(Objective),[0 1]))
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diagnostic.problem = -4;
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return
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end
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if nargin < 3 || isempty(options)
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options = sdpsettings;
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end
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% Initialize the lower bound
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% Typically a good guess
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lower = 0;
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% Silly upper bound
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bestUpper = inf;
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% Create an optimizer object which solves feasibility problem for a
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% particular value of the sought variable
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x = recover(setdiff(depends(Constraints),depends(Objective)));
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if isempty(options) || isequal(options.solver,'')
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% We must figure out suitable solver
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[~,~,~,model] = export(replace(Constraints,Objective,pi));
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options.solver = model.solver.tag;
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end
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P = optimizer(Constraints,[],options,Objective,x);
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% Safe-guard aganst using LMILAB
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if ~isempty(strfind(struct(P).model.options.solver,'lmilab'))
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disp('Selected solver LMILAB lacks features making it unsuitable for BISECTION')
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disp('See why here https://yalmip.github.io/solver/lmilab/');
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disp('Select another SDP solver or/and install a better SDP solver');
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error('Cannot proceed due to poor SDP solver');
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return
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end
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if options.verbose;
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disp(['Selected solver: ' options.solver]);
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fprintf(['Generating initial bound: ' num2str(lower*the_sign)]);
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end
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% Make sure we actually can solve the lower problem
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solvertime = tic;
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[sol, flag] = P{lower};
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diagnostic.solvertime = diagnostic.solvertime + toc(solvertime);
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if flag == 1
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% This was infeasible, hernce we can use it as an upper bound
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i = 1;
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while flag
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bestUpper = lower;
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lower = lower - 2^(-4+i);i = i+1;
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if options.verbose;
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fprintf([' (fail), ' num2str(lower*the_sign)]);
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end
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try
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solvertime = tic;
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[sol, flag] = P{lower};
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diagnostic.solvertime = diagnostic.solvertime + toc(solvertime);
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if lower < -1e6
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if options.verbose;
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fprintf([' (fail). Giving up, never feasible\n']);
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end
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diagnostic.problem = 21;
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diagnostic.info = yalmiperror(diagnostic.problem,'BISECTION');
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return
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end
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catch
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diagnostic.problem = 1;
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diagnostic.info = yalmiperror(diagnostic.problem,'BISECTION');
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return
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end
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end
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if options.verbose;
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fprintf([' (ok).']);
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end
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elseif flag == 0
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else
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diagnostic.problem = flag;
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diagnostic.info = yalmiperror(diagnostic.problem,'BISECTION');
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return
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end
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v = sol;
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optimal = lower;
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upper = bestUpper;
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if isinf(upper)
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upper = lower+1;
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if options.verbose;
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fprintf([' (ok), ' num2str(upper*the_sign)]);
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end
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[sol, flag] = P{upper};
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i = 1;
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while ~flag
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upper = upper + 2^i;i = i+1;
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try
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solvertime = tic;
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if options.verbose;
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fprintf([' (ok), ' num2str(upper*the_sign)]);
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end
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[sol, flag] = P{upper};
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diagnostic.solvertime = diagnostic.solvertime + toc(solvertime);
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catch
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upper
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diagnostic.problem = -1;
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diagnostic.info = yalmiperror(diagnostic.problem,'BISECTION');
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return
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end
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if upper > 1e6
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if options.verbose;
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fprintf([' (oj). Giving up, always feasible!\n']);
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end
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diagnostic.problem = 2;
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diagnostic.info = yalmiperror(diagnostic.problem,'BISECTION');
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return
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end
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end
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if options.verbose;
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fprintf([' (fail).']);
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end
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end
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if options.verbose
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fprintf(['\n']);
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end
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% Perform bisection
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iter = 1;
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if options.verbose
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disp('Iteration Lower bound Test Upper bound Gap Solver status at test');
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end
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working_sol = [];
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while upper - lower > options.bisection.absgaptol
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test = (upper + lower)/2;
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solvertime = tic;
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[sol, flag] = P{test};
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diagnostic.solvertime = diagnostic.solvertime + toc(solvertime);
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if options.verbose;
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if options.bisection.switchedsign
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L = -upper;
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T = -test;
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U = -lower;
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else
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L = lower;
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T = test;
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U = upper;
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end
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if flag
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if flag~=1 && ~any(isnan(sol))
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assign(x,sol);assign(Objective,test);res = check(Constraints);
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if min(res) >= -1e-6
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fprintf(' %4.0f : %12.5E %12.5E %12.5E %12.5E %s\n',iter,L,T,U,U-L,[yalmiperror(flag) '(looks ok)'] );
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flag = 0;
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else
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fprintf(' %4.0f : %12.5E %12.5E %12.5E %12.5E %s\n',iter,L,T,U,U-L,[yalmiperror(flag) '(assumed infeasible)']);
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end
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else
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fprintf(' %4.0f : %12.5E %12.5E %12.5E %12.5E %s\n',iter,L,T, U,U-L,yalmiperror(flag));
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end
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else
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fprintf(' %4.0f : %12.5E %12.5E %12.5E %12.5E %s\n',iter,L,T, U,U-L,yalmiperror(flag));
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end
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end
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if flag == 0
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working_sol = sol;
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optimal = test;
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lower = test;
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else
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upper = test;
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end
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iter = iter + 1;
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end
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if options.bisection.switchedsign
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optimal = -optimal;
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end
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if isempty(working_sol)
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diagnostic.problem = 1;
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else
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% Assign computed solution
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assign(x,working_sol);
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assign(Objective,optimal);
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end
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if options.verbose
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if diagnostic.problem==0
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disp(['Bisection terminated successfully with objective ' num2str(optimal)]);
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end
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end
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