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matlab优化函数（比如fmincon）的具体实现代码能不能看到已有1人参与
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matlab优化函数（比如fmincon）的具体实现代码能不能看到，如果不能的话，cpex的算法具体代码有办法看到吗？想学习这些成熟软件的算法实现代码 |
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wurongjun
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2楼2016-05-27 18:24:41
3楼2016-05-27 23:33:51
wurongjun
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小木虫: 金币+0.5, 给个红包，谢谢回帖
小木虫: 金币+0.5, 给个红包，谢谢回帖
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内置函数的看不到! 这个可以看到啊! function [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = fmincon(FUN,X,A,B,Aeq,Beq,LB,UB,NONLCON,options,varargin) %FMINCON Finds the constrained minimum of a function of several variables. % FMINCON solves 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 % % 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 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=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 the structure OPTIONS, % an argument created with the OPTIMSET function. See OPTIMSET for details. Used % options are Display, TolX, TolFun, TolCon, DerivativeCheck, Diagnostics, GradObj, % GradConstr, Hessian, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, % LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX, Hessian, HessMult, % HessPattern. Use the GradObj option to specify that FUN also returns a second % output argument G that is the partial derivatives of the function df/dX, at the % point X. Use the Hessian option to specify that FUN also returns a third output % argument H that is the 2nd partial derivatives of the function (the Hessian) at the % point X. The Hessian is only used by the large-scale method, not the % line-search method. Use the GradConstr option to specify that NONLCON also % returns third and fourth output arguments GC and GCeq, where GC is the partial % derivatives of the constraint vector of inequalities C, and GCeq is the partial % derivatives of the constraint vector of equalities Ceq. Use OPTIONS = [] as a % place holder if no options are set. % % X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS,P1,P2,...) passes the % problem-dependent parameters P1,P2,... directly to the functions FUN % and NONLCON: feval(FUN,X,P1,P2,...) and feval(NONLCON,X,P1,P2,...). Pass % empty matrices for A, B, Aeq, Beq, OPTIONS, LB, UB, and NONLCON to use the % default values. % % [X,FVAL]=FMINCON(FUN,X0,...) returns the value of the objective % function FUN at the solution X. % % [X,FVAL,EXITFLAG]=FMINCON(FUN,X0,...) returns a string EXITFLAG that % describes the exit condition of FMINCON. % If EXITFLAG is: % > 0 then FMINCON converged to a solution X. % 0 then the maximum number of function evaluations was reached. % < 0 then FMINCON did not converge to a solution. % % [X,FVAL,EXITFLAG,OUTPUT]=FMINCON(FUN,X0,...) returns a structure % OUTPUT with the number of iterations taken in OUTPUT.iterations, the number % of function evaluations in OUTPUT.funcCount, the algorithm used in % OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, % and the first-order optimality (if used) in OUTPUT.firstorderopt. % % [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 HESSIAN of FUN at the solution 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 inline object: % X = fmincon(inline('3*sin(x(1))+exp(x(2))'),[1;1],[],[],[],[],[0 0]) % returns X = [0;0]. % % See also OPTIMSET, FMINUNC, FMINBND, FMINSEARCH, @, INLINE. % Copyright 1990-2001 The MathWorks, Inc. % $Revision: 1.27 $ $Date: 2001/04/06 19:26:10 $ defaultopt = struct('Display','final','LargeScale','on', ... 'TolX',1e-6,'TolFun',1e-6,'TolCon',1e-6,'DerivativeCheck','off',... 'Diagnostics','off',... 'GradObj','off','GradConstr','off',... 'HessMult',[],...% HessMult [] by default 'Hessian','off','HessPattern','sparse(ones(numberOfVariables))',... 'MaxFunEvals','100*numberOfVariables',... 'MaxSQPIter',Inf,... 'DiffMaxChange',1e-1,'DiffMinChange',1e-8,... 'PrecondBandWidth',0,'TypicalX','ones(numberOfVariables,1)',... 'MaxPCGIter','max(1,floor(numberOfVariables/2))', ... 'TolPCG',0.1,'MaxIter',400); % If just 'defaults' passed in, return the default options in X if nargin==1 & nargout <= 1 & isequal(FUN,'defaults') X = defaultopt; return end large = 'large-scale'; medium = 'medium-scale'; if nargin < 4, error('FMINCON requires at least four input arguments'); 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 =[]; end, end, end, end, end, end if isempty(NONLCON) & isempty(A) & isempty(Aeq) & isempty(UB) & isempty(LB) error('FMINCON is for constrained problems. Use FMINUNC for unconstrained problems.') end if nargout > 4 computeLambda = 1; else computeLambda = 0; end caller='constr'; lenVarIn = length(varargin); XOUT=X(  ;numberOfVariables=length(XOUT); switch optimget(options,'Display',defaultopt,'fast') case {'off','none'} verbosity = 0; case 'iter' verbosity = 2; case 'final' verbosity = 1; otherwise verbosity = 1; end % Set to column vectors B = B( ;Beq = Beq( ;[XOUT,l,u,msg] = checkbounds(XOUT,LB,UB,numberOfVariables); if ~isempty(msg) EXITFLAG = -1; [FVAL,OUTPUT,LAMBDA,GRAD,HESSIAN] = deal([]); X( =XOUT;if verbosity > 0 disp(msg) end return end lFinite = l(~isinf(l)); uFinite = u(~isinf(u)); meritFunctionType = 0; mtxmpy = optimget(options,'HessMult',defaultopt,'fast'); if isequal(mtxmpy,'hmult') warnstr = sprintf('%s\n%s\n%s\n', ... 'Potential function name clash with a Toolbox helper function:',... 'Use a name besides ''hmult'' for your HessMult function to',... 'avoid errors or unexpected results.'); warning(warnstr) end diagnostics = isequal(optimget(options,'Diagnostics',defaultopt,'fast'),'on'); gradflag = strcmp(optimget(options,'GradObj',defaultopt,'fast'),'on'); hessflag = strcmp(optimget(options,'Hessian',defaultopt,'fast'),'on'); if isempty(NONLCON) constflag = 0; else constflag = 1; end gradconstflag = strcmp(optimget(options,'GradConstr',defaultopt,'fast'),'on'); line_search = strcmp(optimget(options,'LargeScale',defaultopt,'fast'),'off'); % 0 means trust-region, 1 means line-search % Convert to inline function as needed if ~isempty(FUN) % will detect empty string, empty matrix, empty cell array [funfcn, msg] = optimfcnchk(FUN,'fmincon',length(varargin),gradflag,hessflag); else errmsg = sprintf('%s\n%s', ... 'FUN must be a function or an inline object;', ... ' or, FUN may be a cell array that contains these type of objects.'); error(errmsg) end if constflag % NONLCON is non-empty [confcn, msg] = optimfcnchk(NONLCON,'fmincon',length(varargin),gradconstflag,[],1); else confcn{1} = ''; end [rowAeq,colAeq]=size(Aeq); % if only l and u then call sfminbx if ~line_search & isempty(NONLCON) & isempty(A) & isempty(Aeq) & gradflag OUTPUT.algorithm = large; % if only Aeq beq and Aeq has as many columns as rows, then call sfminle elseif ~line_search & isempty(NONLCON) & isempty(A) & isempty(lFinite) & isempty(uFinite) & gradflag ... & colAeq >= rowAeq OUTPUT.algorithm = large; elseif ~line_search warning(['Large-scale (trust region) method does not currently solve this type of problem,',... sprintf('\n'), 'switching to medium-scale (line search).']) if isequal(funfcn{1},'fungradhess') funfcn{1}='fungrad'; warnstr = sprintf('%s\n%s\n', ... 'Medium-scale method is a Quasi-Newton method and does not use',... 'analytic Hessian. Hessian flag in options will be ignored.'); warning(warnstr) elseif isequal(funfcn{1},'fun_then_grad_then_hess') funfcn{1}='fun_then_grad'; warnstr = sprintf('%s\n%s\n', ... 'Medium-scale method is a Quasi-Newton method and does not use',... 'analytic Hessian. Hessian flag in options will be ignored.'); warning(warnstr) end hessflag = 0; OUTPUT.algorithm = medium; elseif line_search OUTPUT.algorithm = medium; if issparse(Aeq) | issparse(A) warning('Cannot use sparse matrices with medium-scale method: converting to full.') end if line_search & hessflag % conflicting options hessflag = 0; warnstr = sprintf('%s\n%s\n', ... 'Medium-scale method is a Quasi-Newton method and does not use analytic Hessian.',... 'Hessian flag in options will be ignored (user-supplied Hessian will not be used).'); warning(warnstr) if isequal(funfcn{1},'fungradhess') funfcn{1}='fungrad'; elseif isequal(funfcn{1},'fun_then_grad_then_hess') funfcn{1}='fun_then_grad'; end end % else call nlconst else error('Unrecognized combination of OPTIONS flags and calling sequence.') end lenvlb=length(l); lenvub=length(u); if isequal(OUTPUT.algorithm,medium) CHG = 1e-7*abs(XOUT)+1e-7*ones(numberOfVariables,1); i=1:lenvlb; lindex = XOUT(i)<l(i); if any(lindex), XOUT(lindex)=l(lindex)+1e-4; end i=1:lenvub; uindex = XOUT(i)>u(i); if any(uindex) XOUT(uindex)=u(uindex); CHG(uindex)=-CHG(uindex); end X( = XOUT;else arg = (u >= 1e10); arg2 = (l <= -1e10); u(arg) = inf*ones(length(arg(arg>0)),1); l(arg2) = -inf*ones(length(arg2(arg2>0)),1); if min(min(u-XOUT),min(XOUT-l)) < 0, XOUT = startx(u,l); X( = XOUT;end end % Evaluate function GRAD=zeros(numberOfVariables,1); HESS = []; switch funfcn{1} case 'fun' try f = feval(funfcn{3},X,varargin{:}); catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective function', ... ' failed with the following error:', lasterr); error(errmsg); end case 'fungrad' try [f,GRAD( ] = feval(funfcn{3},X,varargin{:});catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective function', ... ' failed with the following error:', lasterr); error(errmsg); end case 'fungradhess' try [f,GRAD( ,HESS] = feval(funfcn{3},X,varargin{:});catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective function', ... ' failed with the following error:', lasterr); error(errmsg); end case 'fun_then_grad' try f = feval(funfcn{3},X,varargin{:}); catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective function', ... ' failed with the following error:', lasterr); error(errmsg); end try GRAD( = feval(funfcn{4},X,varargin{:});catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective gradient function', ... ' failed with the following error:', lasterr); error(errmsg); end case 'fun_then_grad_then_hess' try f = feval(funfcn{3},X,varargin{:}); catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective function', ... ' failed with the following error:', lasterr); error(errmsg); end try GRAD( = feval(funfcn{4},X,varargin{:});catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective gradient function', ... ' failed with the following error:', lasterr); error(errmsg); end try HESS = feval(funfcn{5},X,varargin{:}); catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied objective Hessian function', ... ' failed with the following error:', lasterr); error(errmsg); end otherwise error('Undefined calltype in FMINCON'); end % Evaluate constraints switch confcn{1} case 'fun' try [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:}); c = ctmp( ; ceq = ceqtmp(;cGRAD = zeros(numberOfVariables,length(c)); ceqGRAD = zeros(numberOfVariables,length(ceq)); catch if findstr(xlate('Too many output arguments'),lasterr) if isa(confcn{3},'inline') errmsg = sprintf('%s%s%s\n%s\n%s\n%s', ... 'The inline function ',formula(confcn{3}),' representing the constraints',... ' must return two outputs: the nonlinear inequality constraints and', ... ' the nonlinear equality constraints. At this time, inline objects may',... ' only return one output argument: use an M-file function instead.'); elseif isa(confcn{3},'function_handle') errmsg = sprintf('%s%s%s\n%s%s', ... 'The constraint function ',func2str(confcn{3}),' must return two outputs:',... ' the nonlinear inequality constraints and', ... ' the nonlinear equality constraints.'); else errmsg = sprintf('%s%s%s\n%s%s', ... 'The constraint function ',confcn{3},' must return two outputs:',... ' the nonlinear inequality constraints and', ... ' the nonlinear equality constraints.'); end error(errmsg) else errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied nonlinear constraint function', ... ' failed with the following error:', lasterr); error(errmsg); end end case 'fungrad' try [ctmp,ceqtmp,cGRAD,ceqGRAD] = feval(confcn{3},X,varargin{:}); c = ctmp( ; ceq = ceqtmp(;catch errmsg = sprintf('%s\n%s\n\n%s',... 'FMINCON cannot continue because user supplied nonlinear constraint function', ... ' failed with the following error:', lasterr); error(errmsg); end case 'fun_then_grad' try [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:}); c = ctmp( ; ceq = ceqtmp(;[cGRAD,ceqGRAD] = feval(confcn{4},X,varargin{:}); catch errmsg = sprintf('%s\n%s%s\n\n%s',... 'FMINCON cannot continue because user supplied nonlinear constraint function', ... 'or nonlinear constraint gradient function',... ' failed with the following error:', lasterr); error(errmsg); end case '' c=[]; ceq =[]; cGRAD = zeros(numberOfVariables,length(c)); ceqGRAD = zeros(numberOfVariables,length(ceq)); otherwise error('Undefined calltype in FMINCON'); end non_eq = length(ceq); non_ineq = length(c); [lin_eq,Aeqcol] = size(Aeq); [lin_ineq,Acol] = size(A); [cgrow, cgcol]= size(cGRAD); [ceqgrow, ceqgcol]= size(ceqGRAD); eq = non_eq + lin_eq; ineq = non_ineq + lin_ineq; if ~isempty(Aeq) & Aeqcol ~= numberOfVariables error('Aeq has the wrong number of columns.') end if ~isempty(A) & Acol ~= numberOfVariables error('A has the wrong number of columns.') end if cgrow~=numberOfVariables & cgcol~=non_ineq error('Gradient of the nonlinear inequality constraints is the wrong size.') end if ceqgrow~=numberOfVariables & ceqgcol~=non_eq error('Gradient of the nonlinear equality constraints is the wrong size.') end if diagnostics > 0 % Do diagnostics on information so far msg = diagnose('fmincon',OUTPUT,gradflag,hessflag,constflag,gradconstflag,... line_search,options,defaultopt,XOUT,non_eq,... non_ineq,lin_eq,lin_ineq,l,u,funfcn,confcn,f,GRAD,HESS,c,ceq,cGRAD,ceqGRAD); end % call algorithm if isequal(OUTPUT.algorithm,medium) [X,FVAL,lambda,EXITFLAG,OUTPUT,GRAD,HESSIAN]=... nlconst(funfcn,X,l,u,full(A),B,full(Aeq),Beq,confcn,options,defaultopt, ... verbosity,gradflag,gradconstflag,hessflag,meritFunctionType,... CHG,f,GRAD,HESS,c,ceq,cGRAD,ceqGRAD,varargin{:}); LAMBDA=lambda; else if (isequal(funfcn{1}, 'fun_then_grad_then_hess') | isequal(funfcn{1}, 'fungradhess')) Hstr=[]; elseif (isequal(funfcn{1}, 'fun_then_grad') | isequal(funfcn{1}, 'fungrad')) n = length(XOUT); Hstr = optimget(options,'HessPattern',defaultopt,'fast'); if ischar(Hstr) if isequal(lower(Hstr),'sparse(ones(numberofvariables))') Hstr = sparse(ones(n)); else error('Option ''HessPattern'' must be a matrix if not the default.') end end end if isempty(Aeq) [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN] = ... sfminbx(funfcn,X,l,u,verbosity,options,defaultopt,computeLambda,f,GRAD,HESS,Hstr,varargin{:}); else [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN] = ... sfminle(funfcn,X,sparse(Aeq),Beq,verbosity,options,defaultopt,computeLambda,f,GRAD,HESS,Hstr,varargin{:}); end end |
4楼2016-05-28 19:00:25
5楼2016-05-28 19:23:48