关闭网站需要多久,SQL如何建网站,怎么做外国网站流量,商标每年要交多少钱1.简述 fmincon函数非线性约束下的最优化问题 fmincon函数#xff0c;既是求最小约束非线性多变量函数 该函数被用于求如下函数的最小值
语法如下:
x fmincon(fun,x0,A,b) x fmincon(fun,x0,A,b,Aeq,beq) x fmincon(fun,x0,A,b,Aeq,beq,lb,ub) x fmincon(fun,x0,A,b,Aeq…1.简述 fmincon函数非线性约束下的最优化问题 fmincon函数既是求最小约束非线性多变量函数 该函数被用于求如下函数的最小值
语法如下:
x fmincon(fun,x0,A,b) x fmincon(fun,x0,A,b,Aeq,beq) x fmincon(fun,x0,A,b,Aeq,beq,lb,ub) x fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon) x fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options) x fmincon(problem) [x,fval] fmincon(…) [x,fval,exitflag] fmincon(…) [x,fval,exitflag,output] fmincon(…) [x,fval,exitflag,output,lambda] fmincon(…) [x,fval,exitflag,output,lambda,grad] fmincon(…) [x,fval,exitflag,output,lambda,grad,hessian] fmincon(…)
对于fmincon函数其exitflag参数中的数字
1、一阶最优性条件满足容许范围 2、X的变化小于容许范围 3、目标函数的变化小于容许范围 4、重要搜索方向小于规定的容许范围并且约束违背小于options.TolCon 5、重要方向导数小于规定的容许范围并且约束违背小于options.TolCon 0、到达最大迭代次数或到达函数评价 -1、算法由输出函数终止 -2、无可行点 、
2.代码 主函数
%% 最小费用问题 x0[1,1,1]; lzeros(1,3); [xo,yo]fmincon(f1219,x0,[],[],[],[],l,[],fcon1219) 子函数
function [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] fmincon(FUN,X,A,B,Aeq,Beq,LB,UB,NONLCON,options,varargin) %FMINCON finds a constrained minimum of a function of several variables. % FMINCON attempts to solve problems of the form: % min F(X) subject to: A*X B, Aeq*X Beq (linear constraints) % X C(X) 0, Ceq(X) 0 (nonlinear constraints) % LB X UB (bounds) % % FMINCON implements four different algorithms: interior point, SQP, % active set, and trust region reflective. Choose one via the option % Algorithm: for instance, to choose SQP, set OPTIONS % optimoptions(fmincon,Algorithm,sqp), and then pass OPTIONS to % FMINCON. % % X FMINCON(FUN,X0,A,B) starts at X0 and finds a minimum X to the % function FUN, subject to the linear inequalities A*X B. FUN accepts % input X and returns a scalar function value F evaluated at X. X0 may be % a scalar, vector, or matrix. % % X FMINCON(FUN,X0,A,B,Aeq,Beq) minimizes FUN subject to the linear % equalities Aeq*X Beq as well as A*X B. (Set A[] and B[] if no % inequalities exist.) % % X FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB) defines a set of lower and upper % bounds on the design variables, X, so that a solution is found 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 FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON) subjects the minimization % to the constraints defined in NONLCON. The function NONLCON accepts X % and returns the vectors C and Ceq, representing the nonlinear % inequalities and equalities respectively. FMINCON minimizes FUN such % that C(X) 0 and Ceq(X) 0. (Set LB [] and/or UB [] if no bounds % exist.) % % X FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS) minimizes with % the default optimization parameters replaced by values in OPTIONS, an % argument created with the OPTIMOPTIONS function. See OPTIMOPTIONS for % details. For a list of options accepted by FMINCON refer to the % documentation. % % X FMINCON(PROBLEM) finds the minimum for PROBLEM. PROBLEM is a % structure with the function FUN in PROBLEM.objective, the start point % in PROBLEM.x0, 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 nonlinear constraint function in PROBLEM.nonlcon, the % options structure in PROBLEM.options, and solver name fmincon in % PROBLEM.solver. Use this syntax to solve at the command line a problem % exported from OPTIMTOOL. % % [X,FVAL] FMINCON(FUN,X0,...) returns the value of the objective % function FUN at the solution X. % % [X,FVAL,EXITFLAG] FMINCON(FUN,X0,...) returns an EXITFLAG that % describes the exit condition. Possible values of EXITFLAG and the % corresponding exit conditions are listed below. See the documentation % for a complete description. % % All algorithms: % 1 First order optimality conditions satisfied. % 0 Too many function evaluations or iterations. % -1 Stopped by output/plot function. % -2 No feasible point found. % Trust-region-reflective, interior-point, and sqp: % 2 Change in X too small. % Trust-region-reflective: % 3 Change in objective function too small. % Active-set only: % 4 Computed search direction too small. % 5 Predicted change in objective function too small. % Interior-point and sqp: % -3 Problem seems unbounded. % % [X,FVAL,EXITFLAG,OUTPUT] FMINCON(FUN,X0,...) returns a structure % OUTPUT with information such as total number of iterations, and final % objective function value. See the documentation for a complete list. % % [X,FVAL,EXITFLAG,OUTPUT,LAMBDA] FMINCON(FUN,X0,...) returns the % Lagrange multipliers at the solution X: LAMBDA.lower for LB, % LAMBDA.upper for UB, LAMBDA.ineqlin is for the linear inequalities, % LAMBDA.eqlin is for the linear equalities, LAMBDA.ineqnonlin is for the % nonlinear inequalities, and LAMBDA.eqnonlin is for the nonlinear % equalities. % % [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD] FMINCON(FUN,X0,...) returns the % value of the gradient of FUN at the solution X. % % [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] FMINCON(FUN,X0,...) % returns the value of the exact or approximate Hessian of the Lagrangian % at X. % % Examples % FUN can be specified using : % X fmincon(humps,...) % In this case, F humps(X) returns the scalar function value F of % the HUMPS function evaluated at X. % % FUN can also be an anonymous function: % X fmincon((x) 3*sin(x(1))exp(x(2)),[1;1],[],[],[],[],[0 0]) % returns X [0;0]. % % If FUN or NONLCON are parameterized, you can use anonymous functions to % capture the problem-dependent parameters. Suppose you want to minimize % the objective given in the function myfun, subject to the nonlinear % constraint mycon, where these two functions are parameterized by their % second argument a1 and a2, respectively. Here myfun and mycon are % MATLAB file functions such as % % function f myfun(x,a1) % f x(1)^2 a1*x(2)^2; % % function [c,ceq] mycon(x,a2) % c a2/x(1) - x(2); % ceq []; % % To optimize for specific values of a1 and a2, first assign the values % to these two parameters. Then create two one-argument anonymous % functions that capture the values of a1 and a2, and call myfun and % mycon with two arguments. Finally, pass these anonymous functions to % FMINCON: % % a1 2; a2 1.5; % define parameters first % options optimoptions(fmincon,Algorithm,interior-point); % run interior-point algorithm % x fmincon((x) myfun(x,a1),[1;2],[],[],[],[],[],[],(x) mycon(x,a2),options) % % See also OPTIMOPTIONS, OPTIMTOOL, FMINUNC, FMINBND, FMINSEARCH, , FUNCTION_HANDLE.
% Copyright 1990-2018 The MathWorks, Inc.
defaultopt struct( ... Algorithm,interior-point, ... AlwaysHonorConstraints,bounds, ... DerivativeCheck,off, ... Diagnostics,off, ... DiffMaxChange,Inf, ... DiffMinChange,0, ... Display,final, ... FinDiffRelStep, [], ... FinDiffType,forward, ... ProblemdefOptions, struct, ... FunValCheck,off, ... GradConstr,off, ... GradObj,off, ... HessFcn,[], ... Hessian,[], ... HessMult,[], ... HessPattern,sparse(ones(numberOfVariables)), ... InitBarrierParam,0.1, ... InitTrustRegionRadius,sqrt(numberOfVariables), ... MaxFunEvals,[], ... MaxIter,[], ... MaxPCGIter,[], ... MaxProjCGIter,2*(numberOfVariables-numberOfEqualities), ... MaxSQPIter,10*max(numberOfVariables,numberOfInequalitiesnumberOfBounds), ... ObjectiveLimit,-1e20, ... OutputFcn,[], ... PlotFcns,[], ... PrecondBandWidth,0, ... RelLineSrchBnd,[], ... RelLineSrchBndDuration,1, ... ScaleProblem,none, ... SubproblemAlgorithm,ldl-factorization, ... TolCon,1e-6, ... TolConSQP,1e-6, ... TolFun,1e-6, ... TolFunValue,1e-6, ... TolPCG,0.1, ... TolProjCG,1e-2, ... TolProjCGAbs,1e-10, ... TolX,[], ... TypicalX,ones(numberOfVariables,1), ... UseParallel,false ... );
% If just defaults passed in, return the default options in X if nargin1 nargout 1 strcmpi(FUN,defaults) X defaultopt; return end
if nargin 10 options []; if nargin 9 NONLCON []; if nargin 8 UB []; if nargin 7 LB []; if nargin 6 Beq []; if nargin 5 Aeq []; if nargin 4 B []; if nargin 3 A []; end end end end end end end end
if nargin 1 if isa(FUN,struct) [FUN,X,A,B,Aeq,Beq,LB,UB,NONLCON,options] separateOptimStruct(FUN); else % Single input and non-structure. error(message(optimlib:fmincon:InputArg)); end end
% No options passed. Set options directly to defaultopt after allDefaultOpts isempty(options);
% Prepare the options for the solver options prepareOptionsForSolver(options, fmincon);
% Check for non-double inputs msg isoptimargdbl(FMINCON, {X0,A,B,Aeq,Beq,LB,UB}, ... X, A, B, Aeq, Beq, LB, UB); if ~isempty(msg) error(optimlib:fmincon:NonDoubleInput,msg); end
% Check for complex X0 if ~isreal(X) error(optimlib:fmincon:ComplexX0, ... getString(message(optimlib:commonMsgs:ComplexX0,Fmincon))); end
% Set options to default if no options were passed. if allDefaultOpts % Options are all default options defaultopt; end
if nargout 4 computeLambda true; else computeLambda false; end
activeSet active-set; sqp sqp; trustRegionReflective trust-region-reflective; interiorPoint interior-point; sqpLegacy sqp-legacy;
sizes.xShape size(X); XOUT X(:); sizes.nVar length(XOUT); % Check for empty X if sizes.nVar 0 error(message(optimlib:fmincon:EmptyX)); end
display optimget(options,Display,defaultopt,fast,allDefaultOpts); flags.detailedExitMsg contains(display,detailed); switch display case {off,none} verbosity 0; case {notify,notify-detailed} verbosity 1; case {final,final-detailed} verbosity 2; case {iter,iter-detailed} verbosity 3; case testing verbosity 4; otherwise verbosity 2; end
% Set linear constraint right hand sides to column vectors % (in particular, if empty, they will be made the correct % size, 0-by-1) B B(:); Beq Beq(:);
% Check for consistency of linear constraints, before evaluating % (potentially expensive) user functions
% Set empty linear constraint matrices to the correct size, 0-by-n if isempty(Aeq) Aeq reshape(Aeq,0,sizes.nVar); end if isempty(A) A reshape(A,0,sizes.nVar); end
[lin_eq,Aeqcol] size(Aeq); [lin_ineq,Acol] size(A); % These sizes checks assume that empty matrices have already been made the correct size if Aeqcol ~ sizes.nVar error(message(optimlib:fmincon:WrongNumberOfColumnsInAeq, sizes.nVar)) end if lin_eq ~ length(Beq) error(message(optimlib:fmincon:AeqAndBeqInconsistent)) end if Acol ~ sizes.nVar error(message(optimlib:fmincon:WrongNumberOfColumnsInA, sizes.nVar)) end if lin_ineq ~ length(B) error(message(optimlib:fmincon:AeqAndBinInconsistent)) end % End of linear constraint consistency check
Algorithm optimget(options,Algorithm,defaultopt,fast,allDefaultOpts);
% Option needed for processing initial guess AlwaysHonorConstraints optimget(options,AlwaysHonorConstraints,defaultopt,fast,allDefaultOpts);
% Determine algorithm user chose via options. (We need this now % to set OUTPUT.algorithm in case of early termination due to % inconsistent bounds.) if ~any(strcmpi(Algorithm,{activeSet, sqp, trustRegionReflective, interiorPoint, sqpLegacy})) error(message(optimlib:fmincon:InvalidAlgorithm)); end OUTPUT.algorithm Algorithm; [XOUT,l,u,msg] checkbounds(XOUT,LB,UB,sizes.nVar); if ~isempty(msg) EXITFLAG -2; [FVAL,LAMBDA,GRAD,HESSIAN] deal([]); OUTPUT.iterations 0; OUTPUT.funcCount 0; OUTPUT.stepsize []; if strcmpi(OUTPUT.algorithm,activeSet) || strcmpi(OUTPUT.algorithm,sqp)|| strcmpi(OUTPUT.algorithm,sqpLegacy) OUTPUT.lssteplength []; else % trust-region-reflective, interior-point OUTPUT.cgiterations []; end if strcmpi(OUTPUT.algorithm,interiorPoint) || strcmpi(OUTPUT.algorithm,activeSet) || ... strcmpi(OUTPUT.algorithm,sqp) || strcmpi(OUTPUT.algorithm,sqpLegacy) OUTPUT.constrviolation []; end OUTPUT.firstorderopt []; OUTPUT.message msg; X(:) XOUT; if verbosity 0 disp(msg) end return end
% Get logical list of finite lower and upper bounds finDiffFlags.hasLBs isfinite(l); finDiffFlags.hasUBs isfinite(u);
lFinite l(finDiffFlags.hasLBs); uFinite u(finDiffFlags.hasUBs);
% Create structure of flags and initial values, initialize merit function % type and the original shape of X. flags.meritFunction 0; initVals.xOrigShape X;
diagnostics strcmpi(optimget(options,Diagnostics,defaultopt,fast,allDefaultOpts),on); funValCheck strcmpi(optimget(options,FunValCheck,defaultopt,fast,allDefaultOpts),on); derivativeCheck strcmpi(optimget(options,DerivativeCheck,defaultopt,fast,allDefaultOpts),on);
% Gather options needed for finitedifferences % Write checked DiffMaxChange, DiffMinChage, FinDiffType, FinDiffRelStep, % GradObj and GradConstr options back into struct for later use options.DiffMinChange optimget(options,DiffMinChange,defaultopt,fast,allDefaultOpts); options.DiffMaxChange optimget(options,DiffMaxChange,defaultopt,fast,allDefaultOpts); if options.DiffMinChange options.DiffMaxChange error(message(optimlib:fmincon:DiffChangesInconsistent, sprintf( %0.5g, options.DiffMinChange ), sprintf( %0.5g, options.DiffMaxChange ))) end % Read in and error check option TypicalX [typicalx,ME] getNumericOrStringFieldValue(TypicalX,ones(numberOfVariables,1), ... ones(sizes.nVar,1),a numeric value,options,defaultopt); if ~isempty(ME) throw(ME) end checkoptionsize(TypicalX, size(typicalx), sizes.nVar); options.TypicalX typicalx; options.FinDiffType optimget(options,FinDiffType,defaultopt,fast,allDefaultOpts); options validateFinDiffRelStep(sizes.nVar,options,defaultopt); options.GradObj optimget(options,GradObj,defaultopt,fast,allDefaultOpts); options.GradConstr optimget(options,GradConstr,defaultopt,fast,allDefaultOpts);
flags.grad strcmpi(options.GradObj,on);
% Notice that defaultopt.Hessian [], so the variable hessian can be empty hessian optimget(options,Hessian,defaultopt,fast,allDefaultOpts); % If calling trust-region-reflective with an unavailable Hessian option value, % issue informative error message if strcmpi(OUTPUT.algorithm,trustRegionReflective) ... ~( isempty(hessian) || strcmpi(hessian,on) || strcmpi(hessian,user-supplied) || ... strcmpi(hessian,off) || strcmpi(hessian,fin-diff-grads) ) error(message(optimlib:fmincon:BadTRReflectHessianValue)) end
if ~iscell(hessian) ( strcmpi(hessian,user-supplied) || strcmpi(hessian,on) ) flags.hess true; else flags.hess false; end
if isempty(NONLCON) flags.constr false; else flags.constr true; end
% Process objective function if ~isempty(FUN) % will detect empty string, empty matrix, empty cell array % constrflag in optimfcnchk set to false because were checking the objective, not constraint funfcn optimfcnchk(FUN,fmincon,length(varargin),funValCheck,flags.grad,flags.hess,false,Algorithm); else error(message(optimlib:fmincon:InvalidFUN)); end
% Process constraint function if flags.constr % NONLCON is non-empty flags.gradconst strcmpi(options.GradConstr,on); % hessflag in optimfcnchk set to false because hessian is never returned by nonlinear constraint % function % % constrflag in optimfcnchk set to true because were checking the constraints confcn optimfcnchk(NONLCON,fmincon,length(varargin),funValCheck,flags.gradconst,false,true); else flags.gradconst false; confcn {,,,,}; end
[rowAeq,colAeq] size(Aeq);
if strcmpi(OUTPUT.algorithm,activeSet) || strcmpi(OUTPUT.algorithm,sqp) || strcmpi(OUTPUT.algorithm,sqpLegacy) % See if linear constraints are sparse and if user passed in Hessian if issparse(Aeq) || issparse(A) warning(message(optimlib:fmincon:ConvertingToFull, Algorithm)) end if flags.hess % conflicting options flags.hess false; warning(message(optimlib:fmincon:HessianIgnoredForAlg, Algorithm)); if strcmpi(funfcn{1},fungradhess) funfcn{1}fungrad; elseif strcmpi(funfcn{1},fun_then_grad_then_hess) funfcn{1}fun_then_grad; end end elseif strcmpi(OUTPUT.algorithm,trustRegionReflective) % Look at constraint type and supplied derivatives, and determine if % trust-region-reflective can solve problem isBoundedNLP isempty(NONLCON) isempty(A) isempty(Aeq); % problem has only bounds and no other constraints isLinEqNLP isempty(NONLCON) isempty(A) isempty(lFinite) ... isempty(uFinite) colAeq rowAeq; if isBoundedNLP flags.grad % if only l and u then call sfminbx elseif isLinEqNLP flags.grad % if only Aeq beq and Aeq has more columns than rows, then call sfminle else linkToDoc addLink(Choosing the Algorithm, optim, helptargets.map, ... choose_algorithm, false); if ~isBoundedNLP ~isLinEqNLP error(message(optimlib:fmincon:ConstrTRR, linkToDoc)) else % The user has a problem that satisfies the TRR constraint % restrictions but they havent supplied gradients. error(message(optimlib:fmincon:GradOffTRR, linkToDoc)) end end end
% Process initial point shiftedX0 false; % boolean that indicates if initial point was shifted if any(strcmpi(OUTPUT.algorithm,{activeSet,sqp, sqpLegacy})) if strcmpi(OUTPUT.algorithm,sqpLegacy) % Classify variables: finite lower bounds, finite upper bounds xIndices classifyBoundsOnVars(l,u,sizes.nVar,false); end % Check that initial point strictly satisfies the bounds on the variables. violatedLowerBnds_idx XOUT(finDiffFlags.hasLBs) l(finDiffFlags.hasLBs); violatedUpperBnds_idx XOUT(finDiffFlags.hasUBs) u(finDiffFlags.hasUBs); if any(violatedLowerBnds_idx) || any(violatedUpperBnds_idx) finiteLbIdx find(finDiffFlags.hasLBs); finiteUbIdx find(finDiffFlags.hasUBs); XOUT(finiteLbIdx(violatedLowerBnds_idx)) l(finiteLbIdx(violatedLowerBnds_idx)); XOUT(finiteUbIdx(violatedUpperBnds_idx)) u(finiteUbIdx(violatedUpperBnds_idx)); X(:) XOUT; shiftedX0 true; end elseif strcmpi(OUTPUT.algorithm,trustRegionReflective) % % If components of initial x not within bounds, set those components % of initial point to a box-centered point % if isempty(Aeq) arg (u 1e10); arg2 (l -1e10); u(arg) inf; l(arg2) -inf; xinitOutOfBounds_idx XOUT l | XOUT u; if any(xinitOutOfBounds_idx) shiftedX0 true; XOUT startx(u,l,XOUT,xinitOutOfBounds_idx); X(:) XOUT; end else % Phase-1 for sfminle nearest feas. pt. to XOUT. Dont print a % message for this change in X0 for sfminle. XOUT feasibl(Aeq,Beq,XOUT); X(:) XOUT; end
elseif strcmpi(OUTPUT.algorithm,interiorPoint) % Variables: fixed, finite lower bounds, finite upper bounds xIndices classifyBoundsOnVars(l,u,sizes.nVar,true); % If honor bounds mode, then check that initial point strictly satisfies the % simple inequality bounds on the variables and exactly satisfies fixed variable % bounds. if strcmpi(AlwaysHonorConstraints,bounds) || strcmpi(AlwaysHonorConstraints,bounds-ineqs) violatedFixedBnds_idx XOUT(xIndices.fixed) ~ l(xIndices.fixed); violatedLowerBnds_idx XOUT(xIndices.finiteLb) l(xIndices.finiteLb); violatedUpperBnds_idx XOUT(xIndices.finiteUb) u(xIndices.finiteUb); if any(violatedLowerBnds_idx) || any(violatedUpperBnds_idx) || any(violatedFixedBnds_idx) XOUT shiftInitPtToInterior(sizes.nVar,XOUT,l,u,Inf); X(:) XOUT; shiftedX0 true; end end end
% Display that x0 was shifted in order to honor bounds if shiftedX0 if verbosity 3 if strcmpi(OUTPUT.algorithm,interiorPoint) fprintf(getString(message(optimlib:fmincon:ShiftX0StrictInterior))); fprintf(\n); else fprintf(getString(message(optimlib:fmincon:ShiftX0ToBnds))); fprintf(\n); end end end % Evaluate function initVals.g zeros(sizes.nVar,1); HESSIAN [];
switch funfcn{1} case fun try initVals.f feval(funfcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:ObjectiveError, ... getString(message(optimlib:fmincon:ObjectiveError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end case fungrad try [initVals.f,initVals.g] feval(funfcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:ObjectiveError, ... getString(message(optimlib:fmincon:ObjectiveError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end case fungradhess try [initVals.f,initVals.g,HESSIAN] feval(funfcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:ObjectiveError, ... getString(message(optimlib:fmincon:ObjectiveError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end case fun_then_grad try initVals.f feval(funfcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:ObjectiveError, ... getString(message(optimlib:fmincon:ObjectiveError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end try initVals.g feval(funfcn{4},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:GradientError, ... getString(message(optimlib:fmincon:GradientError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end case fun_then_grad_then_hess try initVals.f feval(funfcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:ObjectiveError, ... getString(message(optimlib:fmincon:ObjectiveError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end try initVals.g feval(funfcn{4},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:GradientError, ... getString(message(optimlib:fmincon:GradientError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end try HESSIAN feval(funfcn{5},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:HessianError, ... getString(message(optimlib:fmincon:HessianError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end otherwise error(message(optimlib:fmincon:UndefinedCallType)); end
% Check that the objective value is a scalar if numel(initVals.f) ~ 1 error(message(optimlib:fmincon:NonScalarObj)) end
% Check that the objective gradient is the right size initVals.g initVals.g(:); if numel(initVals.g) ~ sizes.nVar error(optimlib:fmincon:InvalidSizeOfGradient, ... getString(message(optimlib:commonMsgs:InvalidSizeOfGradient,sizes.nVar))); end
% Evaluate constraints switch confcn{1} case fun try [ctmp,ceqtmp] feval(confcn{3},X,varargin{:}); catch userFcn_ME if strcmpi(MATLAB:maxlhs,userFcn_ME.identifier) error(message(optimlib:fmincon:InvalidHandleNonlcon)) else optim_ME MException(optimlib:fmincon:NonlconError, ... getString(message(optimlib:fmincon:NonlconError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end end initVals.ncineq ctmp(:); initVals.nceq ceqtmp(:); initVals.gnc zeros(sizes.nVar,length(initVals.ncineq)); initVals.gnceq zeros(sizes.nVar,length(initVals.nceq)); case fungrad try [ctmp,ceqtmp,initVals.gnc,initVals.gnceq] feval(confcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:NonlconError, ... getString(message(optimlib:fmincon:NonlconError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end initVals.ncineq ctmp(:); initVals.nceq ceqtmp(:); case fun_then_grad try [ctmp,ceqtmp] feval(confcn{3},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:NonlconError, ... getString(message(optimlib:fmincon:NonlconError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end initVals.ncineq ctmp(:); initVals.nceq ceqtmp(:); try [initVals.gnc,initVals.gnceq] feval(confcn{4},X,varargin{:}); catch userFcn_ME optim_ME MException(optimlib:fmincon:NonlconFunOrGradError, ... getString(message(optimlib:fmincon:NonlconFunOrGradError))); userFcn_ME addCause(userFcn_ME,optim_ME); rethrow(userFcn_ME) end case % No nonlinear constraints. Reshaping of empty quantities is done later % in this file, where both cases, (i) no nonlinear constraints and (ii) % nonlinear constraints that have one type missing (equalities or % inequalities), are handled in one place initVals.ncineq []; initVals.nceq []; initVals.gnc []; initVals.gnceq []; otherwise error(message(optimlib:fmincon:UndefinedCallType)); end
% Check for non-double data typed values returned by user functions if ~isempty( isoptimargdbl(FMINCON, {f,g,H,c,ceq,gc,gceq}, ... initVals.f, initVals.g, HESSIAN, initVals.ncineq, initVals.nceq, initVals.gnc, initVals.gnceq) ) error(optimlib:fmincon:NonDoubleFunVal,getString(message(optimlib:commonMsgs:NonDoubleFunVal,FMINCON))); end
sizes.mNonlinEq length(initVals.nceq); sizes.mNonlinIneq length(initVals.ncineq);
% Make sure empty constraint and their derivatives have correct sizes (not 0-by-0): if isempty(initVals.ncineq) initVals.ncineq reshape(initVals.ncineq,0,1); end if isempty(initVals.nceq) initVals.nceq reshape(initVals.nceq,0,1); end if isempty(initVals.gnc) initVals.gnc reshape(initVals.gnc,sizes.nVar,0); end if isempty(initVals.gnceq) initVals.gnceq reshape(initVals.gnceq,sizes.nVar,0); end [cgrow,cgcol] size(initVals.gnc); [ceqgrow,ceqgcol] size(initVals.gnceq);
if cgrow ~ sizes.nVar || cgcol ~ sizes.mNonlinIneq error(message(optimlib:fmincon:WrongSizeGradNonlinIneq, sizes.nVar, sizes.mNonlinIneq)) end if ceqgrow ~ sizes.nVar || ceqgcol ~ sizes.mNonlinEq error(message(optimlib:fmincon:WrongSizeGradNonlinEq, sizes.nVar, sizes.mNonlinEq)) end
if diagnostics % Do diagnostics on information so far diagnose(fmincon,OUTPUT,flags.grad,flags.hess,flags.constr,flags.gradconst,... XOUT,sizes.mNonlinEq,sizes.mNonlinIneq,lin_eq,lin_ineq,l,u,funfcn,confcn); end
% Create default structure of flags for finitedifferences: % This structure will (temporarily) ignore some of the features that are % algorithm-specific (e.g. scaling and fault-tolerance) and can be turned % on later for the main algorithm. finDiffFlags.fwdFinDiff strcmpi(options.FinDiffType,forward); finDiffFlags.scaleObjConstr false; % No scaling for now finDiffFlags.chkFunEval false; % No fault-tolerance yet finDiffFlags.chkComplexObj false; % No need to check for complex values finDiffFlags.isGrad true; % Scalar objective % For parallel finite difference (if needed) we need to send the function % handles now to the workers. This avoids sending the function handles in % every iteration of the solver. The output from setOptimFcnHandleOnWorkers % is a onCleanup object that will perform cleanup task on the workers. UseParallel optimget(options,UseParallel,defaultopt,fast,allDefaultOpts); ProblemdefOptions optimget(options, ProblemdefOptions,defaultopt,fast,allDefaultOpts); FromSolve false; if ~isempty(ProblemdefOptions) isfield(ProblemdefOptions, FromSolve) FromSolve ProblemdefOptions.FromSolve; end cleanupObj setOptimFcnHandleOnWorkers(UseParallel,funfcn,confcn,FromSolve);
% Check derivatives if derivativeCheck ... % User wants to check derivatives... (flags.grad || ... % of either objective or ... flags.gradconst sizes.mNonlinEqsizes.mNonlinIneq 0) % nonlinear constraint function. validateFirstDerivatives(funfcn,confcn,X, ... l,u,options,finDiffFlags,sizes,varargin{:}); end
% Flag to determine whether to look up the exit msg. flags.makeExitMsg logical(verbosity) || nargout 3;
% call algorithm if strcmpi(OUTPUT.algorithm,activeSet) % active-set defaultopt.MaxIter 400; defaultopt.MaxFunEvals 100*numberofvariables; defaultopt.TolX 1e-6; defaultopt.Hessian off; problemInfo []; % No problem related data [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN]... nlconst(funfcn,X,l,u,full(A),B,full(Aeq),Beq,confcn,options,defaultopt, ... finDiffFlags,verbosity,flags,initVals,problemInfo,varargin{:}); elseif strcmpi(OUTPUT.algorithm,trustRegionReflective) % trust-region-reflective if (strcmpi(funfcn{1}, fun_then_grad_then_hess) || strcmpi(funfcn{1}, fungradhess)) Hstr []; elseif (strcmpi(funfcn{1}, fun_then_grad) || strcmpi(funfcn{1}, fungrad)) n length(XOUT); Hstr optimget(options,HessPattern,defaultopt,fast,allDefaultOpts); if ischar(Hstr) if strcmpi(Hstr,sparse(ones(numberofvariables))) Hstr sparse(ones(n)); else error(message(optimlib:fmincon:InvalidHessPattern)) end end checkoptionsize(HessPattern, size(Hstr), n); end defaultopt.MaxIter 400; defaultopt.MaxFunEvals 100*numberofvariables; defaultopt.TolX 1e-6; defaultopt.Hessian off; % Trust-region-reflective algorithm does not compute constraint % violation as it progresses. If the user requests the output structure, % we need to calculate the constraint violation at the returned % solution. if nargout 3 computeConstrViolForOutput true; else computeConstrViolForOutput false; end if isempty(Aeq) defaultopt.MaxPCGIter max(1,floor(numberOfVariables/2)); [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN] ... sfminbx(funfcn,X,l,u,verbosity,options,defaultopt,computeLambda,initVals.f,initVals.g, ... HESSIAN,Hstr,flags.detailedExitMsg,computeConstrViolForOutput,flags.makeExitMsg,varargin{:}); else defaultopt.MaxPCGIter []; [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN] ... sfminle(funfcn,X,sparse(Aeq),Beq,verbosity,options,defaultopt,computeLambda,initVals.f, ... initVals.g,HESSIAN,Hstr,flags.detailedExitMsg,computeConstrViolForOutput,flags.makeExitMsg,varargin{:}); end elseif strcmpi(OUTPUT.algorithm,interiorPoint) defaultopt.MaxIter 1000; defaultopt.MaxFunEvals 3000; defaultopt.TolX 1e-10; defaultopt.Hessian bfgs; mEq lin_eq sizes.mNonlinEq nnz(xIndices.fixed); % number of equalities % Interior-point-specific options. Default values for lbfgs memory is 10, and % ldl pivot threshold is 0.01 options getIpOptions(options,sizes.nVar,mEq,flags.constr,defaultopt,10,0.01); [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ... initVals.f,initVals.g,initVals.ncineq,initVals.nceq,initVals.gnc,initVals.gnceq,HESSIAN, ... xIndices,options,finDiffFlags,flags.makeExitMsg,varargin{:}); elseif strcmpi(OUTPUT.algorithm,sqp) defaultopt.MaxIter 400; defaultopt.MaxFunEvals 100*numberofvariables; defaultopt.TolX 1e-6; defaultopt.Hessian bfgs; % Validate options used by sqp options getSQPOptions(options,defaultopt,sizes.nVar); % Call algorithm [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] sqpInterface(funfcn,X,full(A),full(B),full(Aeq),full(Beq), ... full(l),full(u),confcn,initVals.f,full(initVals.g),full(initVals.ncineq),full(initVals.nceq), ... full(initVals.gnc),full(initVals.gnceq),sizes,options,finDiffFlags,verbosity,flags.makeExitMsg,varargin{:}); else % sqpLegacy defaultopt.MaxIter 400; defaultopt.MaxFunEvals 100*numberofvariables; defaultopt.TolX 1e-6; defaultopt.Hessian bfgs; % Validate options used by sqp options getSQPOptions(options,defaultopt,sizes.nVar); % Call algorithm [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] sqpLineSearch(funfcn,X,full(A),full(B),full(Aeq),full(Beq), ... full(l),full(u),confcn,initVals.f,full(initVals.g),full(initVals.ncineq),full(initVals.nceq), ... full(initVals.gnc),full(initVals.gnceq),xIndices,options,finDiffFlags, ... verbosity,flags.detailedExitMsg,flags.makeExitMsg,varargin{:}); end
% Force a cleanup of the handle object. Sometimes, MATLAB may % delay the cleanup but we want to be sure it is cleaned up. delete(cleanupObj); 3.运行结果
