matlab非线性拟合程序代码

function [x,h,exitflag,output,lambda,grad,hessian] = fminconset(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options,set,Jmin,varargin); %function [h,x,exitflag,output,lambda,grad,hessian] % = fminconset(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options,set,Jmin,p1,p2,p3 ...); % % Solves constrained minimization problems where some of the variables are % restricted to discrete values. % % The first 10 arguments are as for fmincon (see FMINCON for details): % % The following 2 arguments are special for FMINCONSET: % % Jmin function value of best feasible solution found so far (used to cut the % search tree whenever a higher value is found). Default=Inf. % % set Cell array of allowed set values for each entry in x. % Empty cell if the entry is without set constraint. % Example: for x(1) in {0.1, 0.5, 0.8}, x(2) free and % x(3) in {3.1, 4.0} then % set={[0.1 0.5 0.8],[],[3.1 4]} % % p1,p2,p3 ... Passed to FUN and NONLCON as additional arguments (as for FMINCON) % % Output as for FMINCON: % % x Optimal value of x % h Minimum function value % ... etc as for FMINCON % the values are from the call of FMINCON that gave the optimal feasible solution. % % Algorithm: % % Implements a 'branch-and-bound' method on top of FMINCON and thus the % Optimization Toolbox is required. % The function calls itself recursively. % % The method is intended for problems that are basically continous, with % some variables constrained to sets of standard values. % Made 1992 by: % Ingar Solberg % Institutt for teknisk kybernetikk % Norges Tekniske H�gskole % N-7034 Trondheim % Norway % % Authors address from 1993: % Ingar Solberg Phone: +47 75179152 % Elkem Aluminium Mosj�en Fax: +47 75179676 % N-8655 Mosj�en E-mail: Ingar.Solberg@elkem.no % Norway % revised from the use of CONSTR to the use of FMINCON 1999. % Applies a strategy where the problem is recursively divided into two % subproblems by setting upper and lower bounds on the set-constrained % variables. % global spor; % for testing % Solve problem without set constraints [x,h,exitflag,output,lambda,grad,hessian] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options,varargin{:}); [n,m]=size(set); % spor = [spor; exitflag -h x']; % for testing % check if improvement if h>=Jmin h = inf; % No improvement, no further search along this branch. return end % check if the solution is feasible (except set constraints) if exitflag < 0 h=inf; % Infeasible, no further search along this branch. return; elseif exitflag == 0 disp(['exitflag =',sprintf('%d ',exitflag),' at x= ',sprintf('%e ',x)]); end % check if all set constraints are satisfied k=0; for i=1:m % check x-vector if ~isempty(set{i}) % set constraints applies? % Is it too far away from all values of the set? if ~any(abs(x(i) - set{i}) < optimget(options,'TolX')) k=i; % Violation of this set constraint. break; % Go and split for this x-component end end end if k>0 % some set constraint violated => recursive search needed above=min(find(set{k}>x(k))); % index of smallest set element above x(k) below=max(find(set{k}<x(k))); % index of largest set element below x(k) % Solve first subproblem if it exists if ~isempty(below) ub1=ub; ub1(k)=set{k}(below); % new upper bound on x(k) for 1. subproblem % rather than setting lower and upper bound equal the addition of an extra linear constraint is recommended % in the manual for FMINCON. if ub1(k)==lb(k) Aeq1 = [Aeq; full(sparse(1,k,1,1,size(x,1)))];beq1=[beq;ub1(k)];ub1(k)=inf;lb(k)=-inf; else Aeq1 = Aeq; beq1 = beq; end [x1,h1,exitflag1,output1,lambda1,grad1,hessian1] = fminconset(fun,x,A,b,Aeq1,beq1,lb,ub1,nonlcon,options,set,Jmin,varargin{:}); if h1<Jmin Jmin=h1; % Best so far end else h1=inf; end % Solve second subproblem if it exists if ~isempty(above) lb1=lb; lb1(k)=set{k}(above); % new lower bound on x(k) for 2. subproblem % rather than setting lower and upper bound equal the addition of an extra linear constraint is recommended % in the manual for FMINCON. if lb1(k)==ub(k) Aeq2 = [Aeq; full(sparse(1,k,1,1,size(x,1)))];beq2=[beq;lb1(k)];lb1(k)=-inf;ub(k)=inf; else Aeq2 = Aeq; beq2 = beq; end [x2,h2,exitflag2,output2,lambda2,grad2,hessian2] = fminconset(fun,x,A,b,Aeq2,beq2,lb1,ub,nonlcon,options,set,Jmin,varargin{:}); else h2=inf; end if h1<h2 % Return the best solution h=h1;x=x1;exitflag=exitflag1;output=output1;lambda=lambda1;grad=grad1;hessian=hessian1; else h=h2;x=x2;exitflag=exitflag2;output=output2;lambda=lambda2;grad=grad2;hessian=hessian2; end % spor =[spor;exitflag h x']; % for testing end