MATLAB，优化函数fmincon解析

[x,fval,exitflag,output,lambda,grad,hessian]=fmincon（fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)；

输入参数：fun要求解的函数值；x0函数fun参数值的初始化；

参数值的线性不等式约束A,b

参数值的等式线性约束Aeq,beq,

参数值的上界和下界lb,ub

非线性约束nonlcon

输出参数：X输出最优参数值

Fval输出fun在X参数的值

Exitflag输出fmincon额外条件值

function [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = fmincon(FUN,X,A,B,Aeq,Beq,LB,UB,NONLCON,options,varargin)/*fmincon可以在多元函数中找到最小值FMINCON attempts to solve problems of the form:min F(X)  subject to:  A*X  <= B, Aeq*X  = Beq (linear constraints)线性约束X                     C(X) <= 0, Ceq(X) = 0   (nonlinear constraints)非线性约束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.fmincon函数应用四种不同的算法：内点法（interior point）；序列二次规划算法(SQP)；有效集法（active set）；信赖域有效算法（trust region reflective）。如果采用SQP算法可以设置 OPTIONS = optimoptions('fmincon','Algorithm','sqp')，再把OPTIONS赋给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. The structure PROBLEM must have all the fields.%%   [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 of FMINCON. 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.所有算法中EXITFLAG返回值涵义1  满足一阶最优性条件0函数计算或迭代太多。无法求解-1 被输出和绘图功能阻止-2找不到可行点Trust-region-reflective, interior-point, and sqp:三种算法才有的返回值2  X变化太小Active-set 算法才有的返回值4计算搜索的方向太小5目标函数的预测变化太小。Interior-point and sqp才有的-3  问题没有边界*//*%   [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.返回包含迭代总数和最终目标函数值等信息的结构输出*//*%   [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.返回解x处的拉格朗日乘数：lambda.lower表示lb，lambda.upper表示ub，lambda.ineqlin表示线性不等式，lambda.eqlin表示线性等式，lambda.ineqnonlin表示非线性不等式，lambda.eqnonlin表示非线性不等式。*//*%   [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD] = FMINCON(FUN,X0,...) returns the %   value of the gradient of FUN at the solution X.返回解决方案x的fun渐变值。%*//*  [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = FMINCON(FUN,X0,...) %   returns the value of the exact or approximate Hessian of the Lagrangian%   at X. 返回X的朗格朗日精确解或者近似Hessian矩阵*//* 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 1990-2013 The MathWorks, Inc.*/defaultopt = struct( ...'Algorithm','interior-point', ...'AlwaysHonorConstraints','bounds', ...'DerivativeCheck','off', ...'Diagnostics','off', ...'DiffMaxChange',Inf, ...'DiffMinChange',0, ...'Display','final', ...'FinDiffRelStep', [], ...'FinDiffType','forward', ...    'FunValCheck','off', ...'GradConstr','off', ...'GradObj','off', ...'HessFcn',[], ...'Hessian',[], ...    'HessMult',[], ...'HessPattern','sparse(ones(numberOfVariables))', ...'InitBarrierParam',0.1, ...'InitTrustRegionRadius','sqrt(numberOfVariables)', ...'MaxFunEvals',[], ...'MaxIter',[], ...'MaxPCGIter','max(1,floor(numberOfVariables/2))', ...'MaxProjCGIter','2*(numberOfVariables-numberOfEqualities)', ...    'MaxSQPIter','10*max(numberOfVariables,numberOfInequalities+numberOfBounds)', ...'ObjectiveLimit',-1e20, ...'OutputFcn',[], ...'PlotFcns',[], ...'PrecondBandWidth',0, ...'RelLineSrchBnd',[], ...'RelLineSrchBndDuration',1, ...'ScaleProblem','none', ...'SubproblemAlgorithm','ldl-factorization', ...'TolCon',1e-6, ...'TolConSQP',1e-6, ...    'TolFun',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 Xif nargin==1 && nargout <= 1 && strcmpi(FUN,'defaults')X = defaultopt;returnendif nargin < 10options = [];if nargin < 9NONLCON = [];if nargin < 8UB = [];if nargin < 7LB = [];if nargin < 6Beq = [];if nargin < 5Aeq = [];endendendendendendproblemInput = false;if nargin == 1if isa(FUN,'struct')problemInput = true;[FUN,X,A,B,Aeq,Beq,LB,UB,NONLCON,options] = separateOptimStruct(FUN);else % Single input and non-structure.error(message('optimlib:fmincon:InputArg'));endend% Prepare the options for the solver[options, optionFeedback] = prepareOptionsForSolver(options, 'fmincon');if nargin < 4 && ~problemInputerror(message('optimlib:fmincon:AtLeastFourInputs'))endif isempty(NONLCON) && isempty(A) && isempty(Aeq) && isempty(UB) && isempty(LB)error(message('optimlib:fmincon:ConstrainedProblemsOnly'))end% Check for non-double inputsmsg = isoptimargdbl('FMINCON', {'X0','A','B','Aeq','Beq','LB','UB'}, ...X,  A,  B,  Aeq,  Beq,  LB,  UB);if ~isempty(msg)error('optimlib:fmincon:NonDoubleInput',msg);endif nargout > 4computeLambda = true;else computeLambda = false;endactiveSet = 'medium-scale: SQP, Quasi-Newton, line-search';sqp = 'sequential quadratic programming';trustRegionReflective = 'trust-region-reflective';interiorPoint = 'interior-point';[sizes.xRows,sizes.xCols] = size(X);XOUT = X(:);sizes.nVar = length(XOUT);% Check for empty Xif sizes.nVar == 0error(message('optimlib:fmincon:EmptyX'));enddisplay = optimget(options,'Display',defaultopt,'fast');flags.detailedExitMsg = ~isempty(strfind(display,'detailed'));switch displaycase {'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;otherwiseverbosity = 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-nif isempty(Aeq)Aeq = reshape(Aeq,0,sizes.nVar);endif 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 sizeif Aeqcol ~= sizes.nVarerror(message('optimlib:fmincon:WrongNumberOfColumnsInAeq', sizes.nVar))endif lin_eq ~= length(Beq)error(message('optimlib:fmincon:AeqAndBeqInconsistent'))endif Acol ~= sizes.nVarerror(message('optimlib:fmincon:WrongNumberOfColumnsInA', sizes.nVar))endif lin_ineq ~= length(B)error(message('optimlib:fmincon:AeqAndBinInconsistent'))end% End of linear constraint consistency checkAlgorithm = optimget(options,'Algorithm',defaultopt,'fast'); % Option needed for processing initial guessAlwaysHonorConstraints = optimget(options,'AlwaysHonorConstraints',defaultopt,'fast'); % Determine algorithm user chose via options. (We need this now% to set OUTPUT.algorithm in case of early termination due to % inconsistent bounds.) if strcmpi(Algorithm,'active-set')OUTPUT.algorithm = activeSet;elseif strcmpi(Algorithm,'sqp')OUTPUT.algorithm = sqp;elseif strcmpi(Algorithm,'interior-point')OUTPUT.algorithm = interiorPoint;elseif strcmpi(Algorithm,'trust-region-reflective')OUTPUT.algorithm = trustRegionReflective;elseerror(message('optimlib:fmincon:InvalidAlgorithm'));end    [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)OUTPUT.lssteplength = [];else % trust-region-reflective, interior-pointOUTPUT.cgiterations = [];endif strcmpi(OUTPUT.algorithm,interiorPoint) || strcmpi(OUTPUT.algorithm,activeSet) || ...strcmpi(OUTPUT.algorithm,sqp)OUTPUT.constrviolation = [];endOUTPUT.firstorderopt = [];OUTPUT.message = msg;X(:) = XOUT;if verbosity > 0disp(msg)endreturnend% Get logical list of finite lower and upper boundsfinDiffFlags.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'),'on');funValCheck = strcmpi(optimget(options,'FunValCheck',defaultopt,'fast'),'on');derivativeCheck = strcmpi(optimget(options,'DerivativeCheck',defaultopt,'fast'),'on');% Gather options needed for finitedifferences% Write checked DiffMaxChange, DiffMinChage, FinDiffType, FinDiffRelStep,% GradObj and GradConstr options back into struct for later useoptions.DiffMinChange = optimget(options,'DiffMinChange',defaultopt,'fast');options.DiffMaxChange = optimget(options,'DiffMaxChange',defaultopt,'fast');if options.DiffMinChange >= options.DiffMaxChangeerror(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)endcheckoptionsize('TypicalX', size(typicalx), sizes.nVar);options.TypicalX = typicalx;options.FinDiffType = optimget(options,'FinDiffType',defaultopt,'fast');options = validateFinDiffRelStep(sizes.nVar,options,defaultopt);options.GradObj = optimget(options,'GradObj',defaultopt,'fast');options.GradConstr = optimget(options,'GradConstr',defaultopt,'fast');flags.grad = strcmpi(options.GradObj,'on');% Notice that defaultopt.Hessian = [], so the variable "hessian" can be emptyhessian = optimget(options,'Hessian',defaultopt,'fast'); % If calling trust-region-reflective with an unavailable Hessian option value, % issue informative error messageif 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'))endif ~iscell(hessian) && ( strcmpi(hessian,'user-supplied') || strcmpi(hessian,'on') )flags.hess = true;elseflags.hess = false;endif isempty(NONLCON)flags.constr = false;elseflags.constr = true;end% Process objective functionif ~isempty(FUN)  % will detect empty string, empty matrix, empty cell array% constrflag in optimfcnchk set to false because we're checking the objective, not constraintfunfcn = optimfcnchk(FUN,'fmincon',length(varargin),funValCheck,flags.grad,flags.hess,false,Algorithm);elseerror(message('optimlib:fmincon:InvalidFUN'));end% Process constraint functionif flags.constr % NONLCON is non-emptyflags.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 we're checking the constraintsconfcn = optimfcnchk(NONLCON,'fmincon',length(varargin),funValCheck,flags.gradconst,false,true);elseflags.gradconst = false; confcn = {'','','','',''};end[rowAeq,colAeq] = size(Aeq);if strcmpi(OUTPUT.algorithm,activeSet) || strcmpi(OUTPUT.algorithm,sqp)% See if linear constraints are sparse and if user passed in Hessianif issparse(Aeq) || issparse(A)warning(message('optimlib:fmincon:ConvertingToFull', Algorithm))endif flags.hess % conflicting optionsflags.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';endendelseif strcmpi(OUTPUT.algorithm,trustRegionReflective)% Look at constraint type and supplied derivatives, and determine if% trust-region-reflective can solve problemisBoundedNLP = 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 sfminbxelseif isLinEqNLP && flags.grad% if only Aeq beq and Aeq has more columns than rows, then call sfminleelseif ~isBoundedNLP && ~isLinEqNLPerror(message('optimlib:fmincon:ConstrTRR', ...addLink( 'Choosing the Algorithm', 'choose_algorithm' )))            else% The user has a problem that satisfies the TRR constraint% restrictions but they haven't supplied gradients.error(message('optimlib:fmincon:GradOffTRR', ...addLink( 'Choosing the Algorithm', 'choose_algorithm' )))endendendlenvlb = length(l);lenvub = length(u);% Process initial point shiftedX0 = false; % boolean that indicates if initial point was shiftedif strcmpi(OUTPUT.algorithm,activeSet)%% Ensure starting point lies within bounds%i=1:lenvlb;lindex = XOUT(i)<l(i);if any(lindex)XOUT(lindex)=l(lindex); shiftedX0 = true;endi=1:lenvub;uindex = XOUT(i)>u(i);if any(uindex)XOUT(uindex)=u(uindex);shiftedX0 = true;endX(:) = XOUT;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;endelse% Phase-1 for sfminle nearest feas. pt. to XOUT. Don't print a% message for this change in X0 for sfminle. XOUT = feasibl(Aeq,Beq,XOUT);X(:) = XOUT;endelseif strcmpi(OUTPUT.algorithm,interiorPoint)% Variables: fixed, finite lower bounds, finite upper boundsxIndices = 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;endendelse % SQP% Classify variables: finite lower bounds, finite upper boundsxIndices = classifyBoundsOnVars(l,u,sizes.nVar,false);% SQP always honors the bounds. Check that initial point% strictly satisfies the bounds on the variables.violatedLowerBnds_idx = XOUT(xIndices.finiteLb) < l(xIndices.finiteLb);violatedUpperBnds_idx = XOUT(xIndices.finiteUb) > u(xIndices.finiteUb);if any(violatedLowerBnds_idx) || any(violatedUpperBnds_idx)finiteLbIdx = find(xIndices.finiteLb);finiteUbIdx = find(xIndices.finiteUb);XOUT(finiteLbIdx(violatedLowerBnds_idx)) = l(finiteLbIdx(violatedLowerBnds_idx));XOUT(finiteUbIdx(violatedUpperBnds_idx)) = u(finiteUbIdx(violatedUpperBnds_idx));X(:) = XOUT;shiftedX0 = true;endend% Display that x0 was shifted in order to honor boundsif shiftedX0if verbosity >= 3if strcmpi(OUTPUT.algorithm,interiorPoint) fprintf(getString(message('optimlib:fmincon:ShiftX0StrictInterior')));fprintf('\n');elsefprintf(getString(message('optimlib:fmincon:ShiftX0ToBnds')));fprintf('\n');endendend% Evaluate functioninitVals.g = zeros(sizes.nVar,1);HESSIAN = []; switch funfcn{1}case 'fun'tryinitVals.f = feval(funfcn{3},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:ObjectiveError', ...getString(message('optimlib:fmincon:ObjectiveError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endcase 'fungrad'try[initVals.f,initVals.g] = feval(funfcn{3},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:ObjectiveError', ...getString(message('optimlib:fmincon:ObjectiveError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endcase 'fungradhess'try[initVals.f,initVals.g,HESSIAN] = feval(funfcn{3},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:ObjectiveError', ...getString(message('optimlib:fmincon:ObjectiveError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endcase 'fun_then_grad'tryinitVals.f = feval(funfcn{3},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:ObjectiveError', ...getString(message('optimlib:fmincon:ObjectiveError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endtryinitVals.g = feval(funfcn{4},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:GradientError', ...getString(message('optimlib:fmincon:GradientError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endcase 'fun_then_grad_then_hess'tryinitVals.f = feval(funfcn{3},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:ObjectiveError', ...getString(message('optimlib:fmincon:ObjectiveError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endtryinitVals.g = feval(funfcn{4},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:GradientError', ...getString(message('optimlib:fmincon:GradientError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endtryHESSIAN = feval(funfcn{5},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:HessianError', ...getString(message('optimlib:fmincon:HessianError')));            userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endotherwiseerror(message('optimlib:fmincon:UndefinedCallType'));end% Check that the objective value is a scalarif numel(initVals.f) ~= 1error(message('optimlib:fmincon:NonScalarObj'))end% Check that the objective gradient is the right sizeinitVals.g = initVals.g(:);if numel(initVals.g) ~= sizes.nVarerror('optimlib:fmincon:InvalidSizeOfGradient', ...getString(message('optimlib:commonMsgs:InvalidSizeOfGradient',sizes.nVar)));end% Evaluate constraintsswitch confcn{1}case 'fun'try[ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});catch userFcn_MEif strcmpi('MATLAB:maxlhs',userFcn_ME.identifier)error(message('optimlib:fmincon:InvalidHandleNonlcon'))elseoptim_ME = MException('optimlib:fmincon:NonlconError', ...getString(message('optimlib:fmincon:NonlconError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endendinitVals.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_MEoptim_ME = MException('optimlib:fmincon:NonlconError', ...getString(message('optimlib:fmincon:NonlconError')));           userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endinitVals.ncineq = ctmp(:);initVals.nceq = ceqtmp(:);case 'fun_then_grad'try[ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:NonlconError', ...getString(message('optimlib:fmincon:NonlconError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endinitVals.ncineq = ctmp(:);initVals.nceq = ceqtmp(:);try[initVals.gnc,initVals.gnceq] = feval(confcn{4},X,varargin{:});catch userFcn_MEoptim_ME = MException('optimlib:fmincon:NonlconFunOrGradError', ...getString(message('optimlib:fmincon:NonlconFunOrGradError')));userFcn_ME = addCause(userFcn_ME,optim_ME);rethrow(userFcn_ME)endcase ''% 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 placeinitVals.ncineq = [];initVals.nceq = [];initVals.gnc = [];initVals.gnceq = [];otherwiseerror(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')));endsizes.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);endif isempty(initVals.nceq)initVals.nceq = reshape(initVals.nceq,0,1);endif isempty(initVals.gnc)initVals.gnc = reshape(initVals.gnc,sizes.nVar,0);endif 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.mNonlinIneqerror(message('optimlib:fmincon:WrongSizeGradNonlinIneq', sizes.nVar, sizes.mNonlinIneq))endif ceqgrow ~= sizes.nVar || ceqgcol ~= sizes.mNonlinEqerror(message('optimlib:fmincon:WrongSizeGradNonlinEq', sizes.nVar, sizes.mNonlinEq))endif diagnostics% Do diagnostics on information so fardiagnose('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 nowfinDiffFlags.chkFunEval = false;     % No fault-tolerance yetfinDiffFlags.chkComplexObj = false;  % No need to check for complex valuesfinDiffFlags.isGrad = true;          % Scalar objective% Check derivativesif derivativeCheck && ...               % User wants to check derivatives...(flags.grad || ...                   % of either objective or ...flags.gradconst && sizes.mNonlinEq+sizes.mNonlinIneq > 0) % nonlinear constraint function.validateFirstDerivatives(funfcn,confcn,X, ...l,u,options,finDiffFlags,sizes,varargin{:});end% call algorithmif strcmpi(OUTPUT.algorithm,activeSet) % active-setdefaultopt.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,optionFeedback,varargin{:});elseif strcmpi(OUTPUT.algorithm,trustRegionReflective) % trust-region-reflectiveif (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');if ischar(Hstr) if strcmpi(Hstr,'sparse(ones(numberofvariables))')Hstr = sparse(ones(n));elseerror(message('optimlib:fmincon:InvalidHessPattern'))endendcheckoptionsize('HessPattern', size(Hstr), n);enddefaultopt.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 > 3computeConstrViolForOutput = true;elsecomputeConstrViolForOutput = false;endif isempty(Aeq)[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,optionFeedback,varargin{:});else[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,optionFeedback,varargin{:});endelseif 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 0.01options = 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,optionFeedback,finDiffFlags,varargin{:});else % sqpdefaultopt.MaxIter = 400; defaultopt.MaxFunEvals = '100*numberofvariables'; defaultopt.TolX = 1e-6; defaultopt.Hessian = 'bfgs';% Validate options used by sqpoptions = getSQPOptions(options,defaultopt,sizes.nVar);optionFeedback.detailedExitMsg = flags.detailedExitMsg;% 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,optionFeedback,varargin{:});end