计算机应用网站建设与维护是做什么,wordpress完整迁移,品牌网十大品牌排行榜,网站建设的业务流程图1.简述 linprog函数主要用来求线型规划中的最小值问题#xff08;最大值的镜像问题#xff0c;求最大值只需要加个“-”#xff09;
2. 算法结构及使用方法 针对约束条件为Axb或Ax≤b的问题
2.1 linprog函数 xlinprog(f,A,b) xlinprog(f,A,b,Aeq,beq) xlinprog(f,A,b,Aeq,…1.简述 linprog函数主要用来求线型规划中的最小值问题最大值的镜像问题求最大值只需要加个“-”
2. 算法结构及使用方法 针对约束条件为Axb或Ax≤b的问题
2.1 linprog函数 xlinprog(f,A,b) xlinprog(f,A,b,Aeq,beq) xlinprog(f,A,b,Aeq,beq,lb,ub) xlinprog(f,A,b,Aeq,beq,lb,ub,x0)
2.2 参数简介 f目标函数 A不等式约束条件矩阵 b对应不等式右侧的矩阵 Aeq等式约束条件矩阵 beq不等式右侧的矩阵 Aeq等式约束条件矩阵 beq对应等式右侧的矩阵 lbx的下界 ubx的上界 x0设置初始点x0这个选择项只是对medium-scale算法有效。默认的large-scale算法和简单的算法忽略任何初始点。一般用不到
2.3 常用linprog函数及用法举例 linprog函数常用形式为
xlinprog(f,A,b,Aep,beq,lb,ub); 例子 学习目标有约束条件多元变量函数最小值 适合 计划生产盈利最大 的模式求解 最大值解法可转化为求解最小值算法非常容易 求最大值转化为求最小值 f70*x1120*x2 的最大值当然x1,x2是有约束的。
转化为求 f-(70*x1120*x2) 的最小值。 约束条件9*x14*x23600;4*x15*x22000;3*x110*x23000;-x1,-x2 2.代码 主函数
clc clear f[-70 -120]; A[9 4;4 5;3 10]; B[3600;2000;3000]; Aeq[]; Beq[]; lb[0 0];ub[inf inf]; x0[1 1]; optionsoptimset(display,iter,Tolx,1e-8); [x,f,exitflag]linprog(f,A,B,Aeq,Beq,lb,ub,x0,options) %[xmincon,fval,exitflag,output] fmincon((x)-(70*x(1)120*x(2)),x0,A,B,Aeq,Beq,lb,ub,[],options) 子函数
function [x,fval,exitflag,output,lambda]linprog(f,A,B,Aeq,Beq,lb,ub,x0,options) %LINPROG Linear programming. % X LINPROG(f,A,b) attempts to solve the linear programming problem: % % min f*x subject to: A*x b % x % % X LINPROG(f,A,b,Aeq,beq) solves the problem above while additionally % satisfying the equality constraints Aeq*x beq. (Set A[] and B[] if % no inequalities exist.) % % X LINPROG(f,A,b,Aeq,beq,LB,UB) defines a set of lower and upper % bounds on the design variables, X, so that the solution is in % the range LB X UB. Use empty matrices for LB and UB % if no bounds exist. Set LB(i) -Inf if X(i) is unbounded below; % set UB(i) Inf if X(i) is unbounded above. % % X LINPROG(f,A,b,Aeq,beq,LB,UB,X0) sets the starting point to X0. This % option is only available with the active-set algorithm. The default % interior point algorithm will ignore any non-empty starting point. % % X LINPROG(PROBLEM) finds the minimum for PROBLEM. PROBLEM is a % structure with the vector f in PROBLEM.f, the linear inequality % constraints in PROBLEM.Aineq and PROBLEM.bineq, the linear equality % constraints in PROBLEM.Aeq and PROBLEM.beq, the lower bounds in % PROBLEM.lb, the upper bounds in PROBLEM.ub, the start point % in PROBLEM.x0, the options structure in PROBLEM.options, and solver % name linprog in PROBLEM.solver. Use this syntax to solve at the % command line a problem exported from OPTIMTOOL. % % [X,FVAL] LINPROG(f,A,b) returns the value of the objective function % at X: FVAL f*X. % % [X,FVAL,EXITFLAG] LINPROG(f,A,b) returns an EXITFLAG that describes % the exit condition. Possible values of EXITFLAG and the corresponding % exit conditions are % % 3 LINPROG converged to a solution X with poor constraint feasibility. % 1 LINPROG converged to a solution X. % 0 Maximum number of iterations reached. % -2 No feasible point found. % -3 Problem is unbounded. % -4 NaN value encountered during execution of algorithm. % -5 Both primal and dual problems are infeasible. % -7 Magnitude of search direction became too small; no further % progress can be made. The problem is ill-posed or badly % conditioned. % -9 LINPROG lost feasibility probably due to ill-conditioned matrix. % % [X,FVAL,EXITFLAG,OUTPUT] LINPROG(f,A,b) returns a structure OUTPUT % with the number of iterations taken in OUTPUT.iterations, maximum of % constraint violations in OUTPUT.constrviolation, the type of % algorithm used in OUTPUT.algorithm, the number of conjugate gradient % iterations in OUTPUT.cgiterations ( 0, included for backward % compatibility), and the exit message in OUTPUT.message. % % [X,FVAL,EXITFLAG,OUTPUT,LAMBDA] LINPROG(f,A,b) returns the set of % Lagrangian multipliers LAMBDA, at the solution: LAMBDA.ineqlin for the % linear inequalities A, LAMBDA.eqlin for the linear equalities Aeq, % LAMBDA.lower for LB, and LAMBDA.upper for UB. % % NOTE: the interior-point (the default) algorithm of LINPROG uses a % primal-dual method. Both the primal problem and the dual problem % must be feasible for convergence. Infeasibility messages of % either the primal or dual, or both, are given as appropriate. The % primal problem in standard form is % min f*x such that A*x b, x 0. % The dual problem is % max b*y such that A*y s f, s 0. % % See also QUADPROG.
% Copyright 1990-2018 The MathWorks, Inc.
% If just defaults passed in, return the default options in X
% Default MaxIter, TolCon and TolFun is set to [] because its value depends % on the algorithm. defaultopt struct( ... Algorithm,dual-simplex, ... Diagnostics,off, ... Display,final, ... LargeScale,on, ... MaxIter,[], ... MaxTime, Inf, ... Preprocess,basic, ... TolCon,[],... TolFun,[]);
if nargin1 nargout 1 strcmpi(f,defaults) x defaultopt; return end
% Handle missing arguments if nargin 9 options []; % Check if x0 was omitted and options were passed instead if nargin 8 if isa(x0, struct) || isa(x0, optim.options.SolverOptions) options x0; 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
% Detect problem structure input problemInput false; if nargin 1 if isa(f,struct) problemInput true; [f,A,B,Aeq,Beq,lb,ub,x0,options] separateOptimStruct(f); else % Single input and non-structure. error(message(optim:linprog:InputArg)); end end
% No options passed. Set options directly to defaultopt after allDefaultOpts isempty(options);
% Prepare the options for the solver options prepareOptionsForSolver(options, linprog);
if nargin 3 ~problemInput error(message(optim:linprog:NotEnoughInputs)) end
% Define algorithm strings thisFcn linprog; algIP interior-point-legacy; algDSX dual-simplex; algIP15b interior-point;
% Check for non-double inputs msg isoptimargdbl(upper(thisFcn), {f,A,b,Aeq,beq,LB,UB, X0}, ... f, A, B, Aeq, Beq, lb, ub, x0); if ~isempty(msg) error(optim:linprog:NonDoubleInput,msg); end
% After processing options for optionFeedback, etc., set options to default % if no options were passed. if allDefaultOpts % Options are all default options defaultopt; end
if nargout 3 computeConstrViolation true; computeFirstOrderOpt true; % Lagrange multipliers are needed to compute first-order optimality computeLambda true; else computeConstrViolation false; computeFirstOrderOpt false; computeLambda false; end
% Algorithm check: % If Algorithm is empty, it is set to its default value. algIsEmpty ~isfield(options,Algorithm) || isempty(options.Algorithm); if ~algIsEmpty Algorithm optimget(options,Algorithm,defaultopt,fast,allDefaultOpts); OUTPUT.algorithm Algorithm; % Make sure the algorithm choice is valid if ~any(strcmp({algIP; algDSX; algIP15b},Algorithm)) error(message(optim:linprog:InvalidAlgorithm)); end else Algorithm algDSX; OUTPUT.algorithm Algorithm; end
% Option LargeScale off is ignored largescaleOn strcmpi(optimget(options,LargeScale,defaultopt,fast,allDefaultOpts),on); if ~largescaleOn [linkTag, endLinkTag] linkToAlgDefaultChangeCsh(linprog_warn_largescale); warning(message(optim:linprog:AlgOptsConflict, Algorithm, linkTag, endLinkTag)); end
% Options setup diagnostics strcmpi(optimget(options,Diagnostics,defaultopt,fast,allDefaultOpts),on); switch optimget(options,Display,defaultopt,fast,allDefaultOpts) case {final,final-detailed} verbosity 1; case {off,none} verbosity 0; case {iter,iter-detailed} verbosity 2; case {testing} verbosity 3; otherwise verbosity 1; end
% Set the constraints up: defaults and check size [nineqcstr,nvarsineq] size(A); [neqcstr,nvarseq] size(Aeq); nvars max([length(f),nvarsineq,nvarseq]); % In case A is empty
if nvars 0 % The problem is empty possibly due to some error in input. error(message(optim:linprog:EmptyProblem)); end
if isempty(f), fzeros(nvars,1); end if isempty(A), Azeros(0,nvars); end if isempty(B), Bzeros(0,1); end if isempty(Aeq), Aeqzeros(0,nvars); end if isempty(Beq), Beqzeros(0,1); end
% Set to column vectors f f(:); B B(:); Beq Beq(:);
if ~isequal(length(B),nineqcstr) error(message(optim:linprog:SizeMismatchRowsOfA)); elseif ~isequal(length(Beq),neqcstr) error(message(optim:linprog:SizeMismatchRowsOfAeq)); elseif ~isequal(length(f),nvarsineq) ~isempty(A) error(message(optim:linprog:SizeMismatchColsOfA)); elseif ~isequal(length(f),nvarseq) ~isempty(Aeq) error(message(optim:linprog:SizeMismatchColsOfAeq)); end
[x0,lb,ub,msg] checkbounds(x0,lb,ub,nvars); if ~isempty(msg) exitflag -2; x x0; fval []; lambda []; output.iterations 0; output.constrviolation []; output.firstorderopt []; output.algorithm ; % not known at this stage output.cgiterations []; output.message msg; if verbosity 0 disp(msg) end return end
if diagnostics % Do diagnostics on information so far gradflag []; hessflag []; constflag false; gradconstflag false; non_eq0;non_ineq0; lin_eqsize(Aeq,1); lin_ineqsize(A,1); XOUTones(nvars,1); funfcn{1} []; confcn{1}[]; diagnose(linprog,OUTPUT,gradflag,hessflag,constflag,gradconstflag,... XOUT,non_eq,non_ineq,lin_eq,lin_ineq,lb,ub,funfcn,confcn); end
% Throw warning that x0 is ignored (true for all algorithms) if ~isempty(x0) verbosity 0 fprintf(getString(message(optim:linprog:IgnoreX0,Algorithm))); end
if strcmpi(Algorithm,algIP) % Set the default values of TolFun and MaxIter for this algorithm defaultopt.TolFun 1e-8; defaultopt.MaxIter 85; [x,fval,lambda,exitflag,output] lipsol(f,A,B,Aeq,Beq,lb,ub,options,defaultopt,computeLambda); elseif strcmpi(Algorithm,algDSX) || strcmpi(Algorithm,algIP15b) % Create linprog options object algoptions optimoptions(linprog, Algorithm, Algorithm); % Set some algorithm specific options if isfield(options, InternalOptions) algoptions setInternalOptions(algoptions, options.InternalOptions); end thisMaxIter optimget(options,MaxIter,defaultopt,fast,allDefaultOpts); if strcmpi(Algorithm,algIP15b) if ischar(thisMaxIter) error(message(optim:linprog:InvalidMaxIter)); end end if strcmpi(Algorithm,algDSX) algoptions.Preprocess optimget(options,Preprocess,defaultopt,fast,allDefaultOpts); algoptions.MaxTime optimget(options,MaxTime,defaultopt,fast,allDefaultOpts); if ischar(thisMaxIter) ... ~strcmpi(thisMaxIter,10*(numberofequalitiesnumberofinequalitiesnumberofvariables)) error(message(optim:linprog:InvalidMaxIter)); end end % Set options common to dual-simplex and interior-point-r2015b algoptions.Diagnostics optimget(options,Diagnostics,defaultopt,fast,allDefaultOpts); algoptions.Display optimget(options,Display,defaultopt,fast,allDefaultOpts); thisTolCon optimget(options,TolCon,defaultopt,fast,allDefaultOpts); if ~isempty(thisTolCon) algoptions.TolCon thisTolCon; end thisTolFun optimget(options,TolFun,defaultopt,fast,allDefaultOpts); if ~isempty(thisTolFun) algoptions.TolFun thisTolFun; end if ~isempty(thisMaxIter) ~ischar(thisMaxIter) % At this point, thisMaxIter is either % * a double that we can set in the options object or % * the default string, which we do not have to set as algoptions % is constructed with MaxIter at its default value algoptions.MaxIter thisMaxIter; end % Create a problem structure. Individually creating each field is quicker % than one call to struct problem.f f; problem.Aineq A; problem.bineq B; problem.Aeq Aeq; problem.beq Beq; problem.lb lb; problem.ub ub; problem.options algoptions; problem.solver linprog; % Create the algorithm from the options. algorithm createAlgorithm(problem.options); % Check that we can run the problem. try problem checkRun(algorithm, problem, linprog); catch ME throw(ME); end % Run the algorithm [x, fval, exitflag, output, lambda] run(algorithm, problem); % If exitflag is {NaN, aString}, this means an internal error has been % thrown. The internal exit code is held in exitflag{2}. if iscell(exitflag) isnan(exitflag{1}) handleInternalError(exitflag{2}, linprog); end
end
output.algorithm Algorithm;
% Compute constraint violation when x is not empty (interior-point/simplex presolve % can return empty x). if computeConstrViolation ~isempty(x) output.constrviolation max([0; norm(Aeq*x-Beq, inf); (lb-x); (x-ub); (A*x-B)]); else output.constrviolation []; end
% Compute first order optimality if needed. This information does not come % from either qpsub, lipsol, or simplex. if exitflag ~ -9 computeFirstOrderOpt ~isempty(lambda) output.firstorderopt computeKKTErrorForQPLP([],f,A,B,Aeq,Beq,lb,ub,lambda,x); else output.firstorderopt []; end 3.运行结果
