linprog.m
功能[x，fval，出口，输出，lampda] = linprog（f，a，b，aeq，beq，lb，ub，x0，选项）％copyright 2021，gurobi优化，llc％linprog一个线性狗万app足彩编程示例使用Gurobi Matlab接口％％此示例基于％MATLAB优化工具箱中定义的LINPROG接口。优化工具箱％是Math Works的注册商标，Inc.％％x = linprog（f，a，b）解决了线性编程问题：%%最小化F'* x％对象受到a * x <= b。大问题的%%，您可以将A作为稀疏矩阵和B作为％稀疏向量传递。%% x = linprog（f，a，b，aeq，beq）解决了问题：%%最小化f'* x％对象受到a * x <= b，％aeq * x == beq。大问题的%%，您可以将AEQ作为稀疏矩阵和BEQ作为％稀疏向量传递。如果不存在不等行，则可以设置A = []和B = []。%% x = linprog（f，a，b，aeq，beq，lb，Ub）解决了问题：%%最小化f'* x％对a * x <= b，％aeq * x == beq，％lb <= x <= UB。％％您可以设置LB（j）= -inf，如果x（j）没有下限，并且Ub（j）= Inf，则x（j）没有上限。 You can set Aeq=[] and beq=[] if no % equalities exist. % % x = LINPROG(f,A,b,Aeq,beq,lb,ub,OPTIONS) solves the problem above % given the specified OPTIONS. Only a subset of possible options have % any effect: % % OPTIONS.Display 'off' or 'none' disables output, % OPTIONS.MaxTime time limit in seconds. % % You can set lb=[] or ub=[] if no bounds exist. % % x = LINPROG(PROBLEM) solves PROBLEM, which is a structure that must % have solver name 'linprog' in PROBLEM.solver. You can also specify % any of the input arguments above using fields PROBLEM.f, PROBLEM.A, ... % % [x,fval] = LINPROG(f,A,b) returns the objective value at the solution. % That is, fval = f'*x. % % [x,fval,exitflag] = LINPROG(f,A,b) returns an exitflag containing the % status of the optimization. The values for exitflag and the % corresponding status codes are: % % 1 converged to a solution (OPTIMAL), % 0 maximum number of iterations reached (ITERATION_LIMIT), % -2 no feasible point found (INFEASIBLE, NUMERIC, ...), % -3 problem is unbounded (UNBOUNDED). % % [x,fval,exitflag,OUTPUT] = LINPROG(f,A,b) returns information about % the optimization. OUTPUT is a structure with the following fields: % % OUTPUT.message Gurobi status code % OUTPUT.constrviolation maximum violation for constraints and bounds % % [x,fval,exitflag,OUTPUT,LAMBDA] = LINPROG(f,A,b) returns the % Lagrangian multipliers at the solution. LAMBDA is a structure with % the following fields: % % LAMBDA.lower multipliers corresponding to x >= lb % LAMBDA.upper multipliers corresponding to x <= ub % LAMBDA.ineqlin multipliers corresponding to A*x <= b % LAMBDA.eqlin multipliers corresponding to Aeq*x == beq % % Initialize missing arguments if nargin == 1 if isa(f,'struct') && isfield(f,'solver') && strcmpi(f.solver,'linprog') [f,A,b,Aeq,beq,lb,ub,x0,options] = probstruct2args(f); else error('PROBLEM should be a structure with valid fields'); end elseif nargin < 3 || nargin > 9 error('LINPROG: the number of input arguments is wrong'); elseif nargin < 9 options = struct(); if nargin == 8 if isa(x0,'struct') || isa(x0,'optim.options.SolverOptions') options = x0; % x0 was omitted and options were passed instead x0 = []; end else x0 = []; if nargin < 7 ub = []; if nargin < 6 lb = []; if nargin < 5 beq = []; if nargin < 4 Aeq = []; end end end end end end % Warn user if x0 argument is ignored if ~isempty(x0) warning('LINPROG will ignore non-empty starting point X0'); end % Build Gurobi model model.obj = f; model.A = [sparse(A); sparse(Aeq)]; % A must be sparse model.sense = [repmat('<',size(A,1),1); repmat('=',size(Aeq,1),1)]; model.rhs = full([b(:); beq(:)]); % rhs must be dense if ~isempty(lb) model.lb = lb; else model.lb = -inf(size(model.A,2),1); % default lb for MATLAB is -inf end if ~isempty(ub) model.ub = ub; end % Extract relevant Gurobi parameters from (subset of) options params = struct(); if isfield(options,'Display') || isa(options,'optim.options.SolverOptions') if any(strcmp(options.Display,{'off','none'})) params.OutputFlag = 0; end end if isfield(options,'MaxTime') || isa(options,'optim.options.SolverOptions') params.TimeLimit = options.MaxTime; end % Solve model with Gurobi result = gurobi(model,params); % Resolve model if status is INF_OR_UNBD if strcmp(result.status,'INF_OR_UNBD') params.DualReductions = 0; warning('Infeasible or unbounded, resolve without dual reductions to determine...'); result = gurobi(model,params); end % Collect results x = []; output.message = result.status; output.constrviolation = []; if isfield(result,'x') x = result.x; if nargout > 3 slack = model.A*x-model.rhs; violA = slack(1:size(A,1)); violAeq = norm(slack((size(A,1)+1):end),inf); viollb = model.lb(:)-x; violub = 0; if isfield(model,'ub') violub = x-model.ub(:); end output.constrviolation = max([0; violA; violAeq; viollb; violub]); end end fval = []; if isfield(result,'objval') fval = result.objval; end if strcmp(result.status,'OPTIMAL') exitflag = 1; % converged to a solution elseif strcmp(result.status,'UNBOUNDED') exitflag = -3; % problem is unbounded elseif strcmp(result.status,'ITERATION_LIMIT') exitflag = 0; % maximum number of iterations reached else exitflag = -2; % no feasible point found end lambda.lower = []; lambda.upper = []; lambda.ineqlin = []; lambda.eqlin = []; if nargout > 4 if isfield(result,'rc') lambda.lower = max(0,result.rc); lambda.upper = -min(0,result.rc); end if isfield(result,'pi') if ~isempty(A) lambda.ineqlin = -result.pi(1:size(A,1)); end if ~isempty(Aeq) lambda.eqlin = -result.pi((size(A,1)+1):end); end end end if isempty(lambda.lower) && isempty(lambda.upper) && ... isempty(lambda.ineqlin) && isempty(lambda.eqlin) lambda = []; end % Local Functions ========================================================= function [f,A,b,Aeq,beq,lb,ub,x0,options] = probstruct2args(s) %PROBSTRUCT2ARGS Get problem structure fields ([] is returned when missing) f = getstructfield(s,'f'); A = getstructfield(s,'Aineq'); b = getstructfield(s,'bineq'); Aeq = getstructfield(s,'Aeq'); beq = getstructfield(s,'beq'); lb = getstructfield(s,'lb'); ub = getstructfield(s,'ub'); x0 = getstructfield(s,'x0'); options = getstructfield(s,'options'); function f = getstructfield(s,field) %GETSTRUCTFIELD Get structure field ([] is returned when missing) if isfield(s,field) f = getfield(s,field); else f = []; end
